In For the Republic Pt. II, is there anyway to do this without killing them, or is that my only option.

...The objective is to blow up their bunker, so I'm assuming there's no peaceful way of blowing up people.

You can always try to deactivate Mr.house.

If you haven't already, try helping to oust Mcnamara, you might get other options from the elder that replaces him.

Problem: I can't find the mission discs. I got the holotapes, though.

I seriously tried to find a peaceful way of resolving this, but alas, I had to blow the place up.

Peaceful resolution is possible. If you give the elder some time to end the lockdown and return, maybe he'll be able to discuss it with you.