The Tavern

I'm in midgame (have one rune). I have teleportitis and haven't found any cure mut potions. I'm in Snake and I can see that this is putting me at high risk of death.

The obvious advice is "find a cure mut potion and drink it quick" - does anyone have any supplementary advice about how to stay alive long enough to achieve that?

Why does one never find one of those pesky -Tele items while afflicted with Teleportitis?
Try training Evocations to teleport away from dangerous situations. Use invisibility. If you need to rest go upstairs first.

Stay out of Snake 5.

You probably mean Snake 4.

Evocable teleportation no longer exists in Trunk, and the OP has the mutation, not a cursed ring.
That said, stay out of branch endings and play extra defensively. Start running earlier, etc, since you never know when you'll be placed into the middle of a mob of enemies.

Also stay out of elf:2 (unless a lot of invisibility) and generally stay out of elf:3.