Aw, fuck!
Maybe look for one of those outdoor throw rugs (since they're made to sit outside and get rained on and such), so if she does so, again, instead of throwing it out, you can hose it off??? If it's just because she's having to hold it a bit too long while you're at work, maybe some peepads?
I'd never used them until last month, but when my cat was recovering from surgery, I decided I would try them. I cannot tell you how much they helped. The poor baby was trying so hard to be a good girl - would get all the way in her litterbox, but then pee over the edge - like she'd expended all her energy getting in the box, and aiming was just too much.