I have heard good things about induction. I keep meaning to buy a small countertop cooker. I mean, the good thing about gas is it works in a power outage (thankfully rare).

but I still have to actually make my meals in the kitchen (KITCHEN!) which is right next to the room where they are sleeping on the couch. With no separating door.

Not ideal. I was going to suggest a pedestal fan night be useful, or chucking a blanket up between the rooms? Might help with privacy/light too.