I'm in the same boat. We do playtime in the middle of the living room. It brings us so much fun and them too that we just work around the annoyances. I lay on the couch and sip my favorite wine and nibble cheese and watch the pigs at play every Friday night. I know, I'm a happen'n, wild 20-something living the hip urban downtown life.
Anyway! I use almost the same things as you. I set up a thin king sized mattress pad over a vinyl shower curtain, then put them pen on the edges of it.
Afterwards, I just pick up the pad and dump the hay and poo off the balcony onto the city parking lot behind me. I'd feel bad about this but it all blows away within minutes. It's...natural! Then I use the hand vac quickly on the area. Sometimes it feels like a pain but it really only takes a few minutes.