Been working on a reasonably priced Muldrotha, the Gravetide deck for a while now that is more about fun/janky combos than exploiting the commander's ability to win in 5 turns. The appealing thing about Muldrotha as a commander for me was that you can self mill yourself to reliably tutor all the pieces needed for a million different combos ranging from concise (infinite mana plus Exsanguinate)) to silly (Grozoth to a handful of 9 drop bombs). When I first started building this I incorporated a lot of (way too many) tutors and transmute cards. In play testing I really found that most transmute effects were too mana costly and really screwed up the tempo of the deck and made it difficult to remember which cards to grab when I had the chance. The cornerstone of this deck is to setup lots of fun combos and to use Muldrotha's ability along with lots of ramp, infinite mana combos, and tutoring to reliably and relatively quickly pull them off. The combos in the deck are, to the best of my ability, built around being able to use different cards to achieve the same result so that you can build an EDH deck with reliability more like a modern one. I've broken out each major area below:
Ramp
Muldrotha enabling Green cards in this deck is focused almost entirely on using them to ramp but also to lean towards cards that allow a Necrotic Ooze infinite combo. We sacrifice some earlier dropping mana dorks for mana dorks that provide greater utility in turns 4+
Untap mechanics from Krosan Restorer and Argothian Elder increase the efficacy of bounce lands (now worth 4 each from the 2x tap) as well as lands enchanted by Market Festival or Dawn's Reflection. Additionally if you can enchant a bounce land you can produce 8 mana per land. Stone-Seeder Hierophant does the best job of this (a friend of mine abuses this combo shamelessly in EDH) but requires, "play additional land this turn," effects to work. Krosan and Argothian are also combo pieces in the later game to Necrotic Ooze and can be chump blocked or sac'd with Ashnod's Altar for pinch mana.
Standard budget artifact ramp, have to have a Sol Ring and Gilded Lotus helps mana fix. Obviously the ideal is turn one Sol Ring into any of the signets, if you get a ramp or a dork out on turn two and make your land drops you can have Muldrotha out on turn 3.
Tutors
I consider Muldrotha, the Gravetide to basically be a really great tutor card and her ability hugely increases the reliability of pulling off all the fun combos later on. It's possible to get these combos going very early in the game with the right combination of ramp and tutoring but I've also experienced games where I durdle around and get ignored low risk and then go off on a late game hand and walk away with a win.
For self-mill We use Mirror-Mad Phantasm, Tunnel Vision, Traumatize, and Morality Shift to dump 50-90% of our library into the graveyard in one shot. We protect ourselves from getting milled or self milling by keep Psychic Spiral and Perpetual Timepiece as options, Laboratory Maniac is an obvious wincon here as well.
Additionally we can either grab much needed cards from our library or tutor for a self mill using Demonic Tutor, Diabolic Tutor, and Beseech the Queen. The last of those three is also super helpful to trade damage for ramp if you have it in your starting hand or to grab a card draw option. Additionally Brainspoil pulls double duty as removal and as a tutor for any utility 5 drop like Traumatize or even Peregrine Drake if you are setup for the combo. Grozoth tutors all your 9 drops to your hand if you play him or can be tutored for 1UU to grab Expropriate, Rise of the Dark Realms, In Garruk's Wake, or Artisan of Kozilek in a pinch. You can then cast him back from your graveyard on that extra Expropriate turn.
Targeted Removal and Control
Since this deck tries to get big combos out fast it is vulnerable to some scary early game board states. We make up for that with a lot of removal and by being able to chump block as needed with low cost mana dorks knowing that we can get them back later with Muldrotha.
The black removal classics are here: Go for the Throat, Doomblade and combine with Imprisoned in the Moon and Beast Within to deal with problem children and indestructible. Additionally Acidic Slime, Shriekmaw and Merciless Executioner offer additional removal options and can be sacrificed or chump blocked and pulled back out from the graveyard to trigger again.
Pernicious Deed is ruthless with Muldrotha allowing you to constantly board wipe <=5 drops and then take what you want back of your own from your graveyard with Muldrotha. Capsize, Hinder, and Spell Crumple round our options out and the latter two combo with Tunnel Vision to mill your opponents to 1 card. Reanimate offers options both for yourself and to remove and then grab a great creature from an opponent. Tectonic Edge helps deal with Homeward Path, etc. and has recursion from your graveyard, it is also not a lot of money hence making the cut over Strip Mine but DustBowl is arguably better if you don't mind shelling out $15
Card Draw
Muldrotha offers some interesting card draw options due to a lack of caring about stuff that ends up in your graveyard. This enables things like Fact or Fiction to basically turn into just drawing 5 cards, Forgotten Creation lets you draw a new hand every turn without losing any of the cards you discarded. Baleful Strix does its thing. Prosperity gives card advantage to your opponents as well but if you play it for enough also forces them to discard and actually care about it as opposed to your...not caring.
Fun Combos
Recursion and Utility Combos: Muldrotha enables recursion like no other but only for permanents, there's a couple ways we can also deal with this. I've listed a few of my favorite recursion combos below
1.) Useful ETB ability x Ashnod's Altar: This is everything from sacrificing Peregrine drake to get plus 2 to play it from your graveyard to end up with net 7 mana to pull off an early Deadeye Navigator combo to just sacrificing and recasting Acidic Slime every turn to control the board state or Baleful Strix to draw a card. Plus you can get a decent chunk of your mana back for playing the same card.
2) Shriekmaw, does it on his own - can be cast for 1B for evoke from graveyard every turn as your creature and just returns to the graveyard
3) Scribe of the Mindful or Archaeomancer x Ashnod's Altar to return instants and sorceries
4) Pernicious Deed over and over again
5) Merciless Executioner every turn. He sacrifices himself, if you have him in your hand and Muldrotha out you can play him twice in a turn.
Infinite Mana: We want this, this deck has a number of overlapping options to do this with cards on the battlefield or with cards on the battlefield and the graveyard.
1) Classic Peregrine Drake x Deadeye Navigator I prefer peregrine drake to the other options because it is only a 5 drop, it combos off with getting more than 5 back by untapping double mana bounce lands, and it costs like $0.50
2.) Necrotic Ooze x pila-pala x Any two mana card. These would include Palladium Myr, Argothian Elder, Fyndhorn Elder, Apprentice Wizard or Krosan Restorer with threshold.
3.) Myr Welder x Pili-Pala x Any two mana artifact or artifact creature. Again Palladium Myr, Sol Ring, Worn Powerstone, Gilded Lotus
4) Pili-Pala x Grand Architect or x Myr Welder after exiling Pili-Pala from your Graveyard. These can both be tutored out of your graveyard in one turn for 4 colorless and U with one as your artifact and one as your creature but you either have a very vulnerable turn waiting for summoning sickness to end or need to move Lightning Greaves over.
Game Ending or Player Removing Combos:
1.) 9 Drop Bombs: Infinite mana (or arguably just a late game state with a lot of mana on the board)) to Grozoth into a full hand of Expropriate, In Garruk's Wake, Rise of the Dark Realms, and Artisan of Kozilek. Ideally you tutor It That Betrays because it's fun or Archaeomancer out of your graveyard to play expropriate again.
2) Infinite Mana plus Mill: Any infinite mana combo plus Mind Grind.
3) Infite Mana plus Non-Creature Damage: Any infinite mana combo plus Exsanguinate
4) Counter then Tunnel Vision: Hinder or Spell Crumple then Tunnel Vision that player targeting the card you just countered. Admittedly they would get another turn unless you or someone else forces a draw but if you get this off quickly and/or right you can mill out a threat with a better board state if you can last another turn
5) Infinite Mana plus Card draw: Dump as much as you can in your graveyard then use either Psychic Spiral or Perpetual Timepiece or Morality Shift to return it all to your library. Then declare Prosperity for however much mana mills all your opponents on card draw and leaves you a couple.
6) Mill yourself then swap: Mill yourself terribly then use Psychic Spiral to one shot someone. Downside of this is it takes all that fun stuff out of your library so it isn't super viable unless you have a dominant board state or need to get rid of somebody.
7) Infinite mana plus Capsize duh
8) Artisan of Kozilek into It That Betrays into The Living End. Take everything on the board, give them a bunch of trash from their graveyard! Great way to take all of your opponents commanders at once since it bypasses hexproof and indestructible. Weak to Homeward Path obviously but that's a chance i'm willing to take
9) Infinite Mana x Acidic Slime x Deadeye Navigator, won't get creatures but will board wipe pretty much everything else
Other Stuff
Lands run in this deck are run for the budget aspect, there are better lands but these ones get the job done and are CHEAP. Pretty similar story for commander cover, these is no voltron aspect to this deck so Diplomatic Immunity is great. That and Alpha Authority can easily be pulled back from the graveyard in your enchantment slot if destroyed. Lightning Greaves is just worth the money, an order of magnitude better than Swiftfoot Boots if you don't plan on putting other stuff on your commander.
Conclusion
This deck isn't aiming to be a super competitive monster, but after a lot of time and a lot of losing it I've found it to be a fun way to play Muldrotha.
