Personally I like to keep AMW just for the mana temple but to each their own. Do the crone's quest first anyway since you need to be chaotic for that anyway. No sense losing your piety unless you use Guth for the PoCC. Gather everything before doing that.
Pacifying the big room is more evidence that you've read too much guidebook. It might have been useful when you could use stoma to get multiple precrownings. Even then it was mostly a waste of time/turns. Remember: it shows you everything you can do, not everything you should do.
For ice queen you need invis. Don't kill anything you don't have to. Kill the prince ASAP. Fire magic doesn't work. AMW is useful here too.
Good luck.
Completed: All Races, All Classes. Twice.
Fastest Run: Dwarf Mindcrafter - 34803 turns. No wand of tele.
Challenge Games: C- CK (stupid ending), Platinum Girdle x10, Westside Story, Team Teleport - illiterate troll barb, Scroll of Omnipotence obtained
ULE - DE Archer