I think I also like final parting over dark petition as well here

I’m building this deck and appreciate the thinking put into it. What would you think of Boseiju, Who Shelters All as protection for casting Ad Nauseum and Insidious Dreams, among other sorceries and instants?

Phyrexian Altar works wonder in this deck it can ramp up a lot of mana to cast other cards needed.

What do you think of Mikaeus, the Unhallowed. Is it too expensive?

Jebdioah boseiju would definitely work here !

epajula mikaeus can work here for sure however I cut it because at 6 mana it can be tough to cast at times

Running all my swamps as snow-swamps and using Dead of Winter as a second Toxic Deluge has served me well.

Is Ulamog, the Infinite Gyre a must-run in this deck? If not, what are some alternatives I could run?

I feel like the new "Blood Artist" enchantment Bastion of Remembrance would be good here since it's less susceptible to removal?

Liquimetal Coating could be an ok include for removing enchantments like rest in peace by making them into artifacts and then destroying them with gate to pyhrexia or sword or sinew & steel, it is a two card combo but with enough tutor cards included in the deck it could be viable.

I know you said you cut Mikaeus, but Mike and trike (and maybe hangarback walker) could be decent with the reanimation, entomb effects, and discard outlet attached to Yawgmoth and ads more win con option / flexibility in the event you get Grasped or something else. You could also living death and in response discard mike, trike, or entomb for a piece. Think it's a decent 2 card combo (but ballista is 3 still) vs the normal undying dudes 3 card combo but is definitely more of reanimation targets than hard cast cards. Mikaeus would also allow you to undying combo with any two non-humans so you could maybe fire off an early game win if you can reanimate him with two other non-humans in play if you don't have any other undying creatures in play.

Mike and trike are not good to hit with Ad Nauseum though. Unless you go for that win and need a piece.

Not sure how good this would be in practice though compared to whatever cards would be cut.