Unfortunately, my priority is surviving until a year at this place is up, so that I can quit without potentially being labeled a job hopper. I don't want to damage my career permanently.
Try push-ups and hang-ups at home once per day. You have a floor, so push-ups are always available. Anything strong enough above-head will do for hang-ups: A staircase, with overhead steps you can grab hold off or a horizontal beam. If your landlord is fine with it, you can install a hang-up bar in a doorway.
Someone put those up in our office, including a personal highscore sheet to mark your progress.
This. At the end of the day it's up to you to find/make the time to balance your life out. I've been learning a lot lately about balance, it's more important than I used to think.