The Visitor Event Guide/Discussion.

You don't take cube damage in the res cube though.

Not in the level 60 pq, at least.
When I solo the 60 on two chars, I do the lazer room by taking the shoes off one char to suicide it quickly, and then clearing the room with just one char.
Sometimes I forget to put the shoes back on in the res room, but it never dies again in there, only after being pulled into the next cube.