You don’t need copper tubing, any tubing that’ll hold water will work. There aren’t going to be high temperatures or pressures. The supply won’t be able to go full blast with poly and hose clamps but it wouldn’t need to. I had a whole plan for this in my head then moved somewhere I didn’t need it and never made it happen.
As for a mini spit, that’s the easiest option if the central is shot, if the layout isn’t complicated. But the place isn’t owned by OP so it’s probably a non starter. They don’t even want to fix what’s there it sounds like.