I've been playing MuAKs lately (including my recorded 6 rune YASD) which has been a blast. No food clock, literally sacrifice every corpse you see for mad piety...but you're probably going to need all that piety because, hey you're a mummy.
So yeah, banish anything that is giving you trouble in the early game, especially if it's part of a group or you're on the verge of death. I like banishing orc priests (and wizards as a mummy), hydras, bees, black mambas, spiny frogs, anything dangerous with lowish MR. You don't want to overdo it of course, but it can be a lifesaver. I train my Invo to 11 or 12, as that maxes out banishment and gets the other Lugonu abilities reasonable. Banishment ability definitely becomes more situational as you get deeper and monster MR goes up--but you can still banish giants and such.
I prefer to wear heavier armour as an AK, but of course that's a preference. You've got blink already basically, plus a suite of other amazing abilities unaffected by armour use. You don't really need Spellcasting for some time, and even then I usually just pick up some charms. As a mummy though I was being particularly stringent with my experience budget.
Distortion weapons are beautiful. I was using the Singing Sword but it became outclassed eventually by a demon blade of distortion. Very useful not only for killing things, but also for "this thing needs to not be here right now"--whether by killing it, banishing it, or teleporting it away, the threat is gone. Great for dealing with swarms of enemies, the blinks and teleports give you some breathing room and you can take them more at your own tempo. And with an AK you don't have to be totally committed to it--you can swap out a blowgun, bow, whatever without worry. So it's just another tool in your arsenal. Which reminds me--make sure you do get some other kind of ranged attack, because distortion blinking can get to be pretty annoying. Banishment is an option but you can't use it all the time. I went heavy Evo in my last game with a lightning rod.
Corrupt is the most nuclear weapon at your disposal. I usually use it at the bottom of branches and usually everybody just dies. Makes Vault 5 an utter delight (especially when you're a mummy and you get a friendly tormentor!!) I also used it on Orc 4, Swamp 5, Elf 3, Tomb 3 to good effect...the Tomb 3 was particularly great as it busted into the treasure wings and also summoned a silent spectre. Great for taking out Saint Roka, the Enchantress, Pan Lords, zig floors, anything really. If I'm going to corrupt slime, I'll usually do it BEFORE attempting to banish/kill TRJ, as you can make sure the loot opens up (of course the jellies can get at it too), and also just probably kill TRJ outright in the carnage.
Of course there are limitations...it costs a ton of piety and can only be used once/level, so don't pop it prematurely. The summons can hurt you although won't actively try, so make sure you can take a couple hits or get to some open space if necessary; it's better to use corrupt preemptively at the beginning of a huge battle rather than when you're already at low health. An amulet of warding will cause them to flinch away, so that can be helpful. Finally, be aware that corrupt creatures CAN BE ABJURED...this was the cause of another YASD in elf 3 before I realized this.
I also like to corrupt the temple ASAP. You'll probably want a Lugonu altar eventually, and besides it's just fun and good luck. Lugonu takes great delight in reclaiming the temple from which she has been shunned
One last thing: keep your piety above ***** if you can, because Enter the Abyss is a "don't die" button. It will save your ass, much like Sanctuary. So don't forget about this as a last resort.