From my understanding, Ultima Weapon's HP conversion formula works exactly like it did in FF6 - the damage multiplier is the precentage of health you have. It also ignores slash resistance.
Anyways, resource management in the first five maps of bonus dungeon mostly boils down to a couple of things: equip your characters defensively so they don't need MP to kill most enemies. Regalia, Kagami + Magatama, Transparent Armor (only do this on extremely frail characters that otherwise just can't survive) + Hakurei Ribbon, 90% Divine Barrier for Lithos/Byakuren, et cetera. Also, know how your characters can regenerate MP - every character in the game except Lithos, Aya and Reisen can do so, so make sure you have the resources (ie. get that Sacred Clothes). This means if worst come to worst, you can always leave the evil maps section, go to the area A (where you can run from battles), have Satori petrify some centipedes and spam Guard to recover MP. Speaking of Satori, make good use of her because she's the only character that can easily regenerate large amount of MP on demand, by equipping the Akiba Sacred Cherry Blossom and using Tentacle/Vacuum Wave on some low DEF enemies and/or plants, and she also has access to easy instant death skills which works on half the mobs you will meet. Also, Azoth is a great help - Marisa can in fact achieve 1MP spells with Azoth and the right growth tree arrangements, which is obviously a huge help.
From the sixth map on you will start encountering minibosses. The sixth map gives you mostly stage 21 miniboss * 2 formations, and most of them are not tough, but Guam Cromch or whatever it's named will still give you pain, so having light-elemental attacker here is pretty important. Seventh map consist of single encounters with stage 27 minibosses. Keep in mind Byakuren's Power Down works on half of them (if you can get power down to hit and you have some decent defensive equipment, you can just normal attack until they go away for the most part), and of the half that doesn't work, Yuugi gets slayer on three of them. Seraphim is no threat as long as you carry one dark spell on someone who is normally slower, and use it every turn (The only threatening attack it has is Punish the Judgment, which it won't use unless light land is at max at the beginning of a turn); Dragon Bungee can be dealt with by having Alice giving someone perpetual London Doll coverage and some HP regeneration, LED Mirage can be dealt with via Private Square or defend until it runs out of MP, and Demiurge... can be dealt with F12 :derp: Or use Quicktime and Aya support and hope you can kill him in three turns. (Seriously, if you don't have Quicktime or Aya Support or projected firepower to have a reasonable chance of killing it in three turns, do not try to fight Demiurge.) Eighth map is just an odd mixmatch that it's kind of hard to summarize, but only Dragon is really tough. This is the last map anyways so you can just go all out if you want.