I was hoping this would be an option, thanks for the heads up!
What specifically did you have to do? Is it just a matter of not taking any damage from them while you're in there?
Yup. I thought Power Armor would help, but they just chew right through it. One hit and you get sick.
Don't take a companion, as you'll get sick when they get bitten as well. Just take it easy, save often and check if you're sick before saving. Taking some grenades and a weapon that can blow 'em up quickly helps too. I used an SMG with explosive rounds.
Also, exploit the furniture. When you enter a room, jump on a desk or some boxes so you can stay in the air. Harder for them to attack you.
Just make a few saves at specific points and reload after you've gotten the tropies/achievements if it means that much to you. This is a game about making choices, after all, and there's already so little choices to be made.
It's more forgiving than New Vegas, in that game you got locked into your faction pretty early on.