You might consider one of those outdoor carpets at Wal-Mart. I think I saw one for $40. just today. Just lay that over the other carpet, and remove it whenever you leave. I have laid a carpet over another carpet, and it worked just fine. I laid mine all the way to the wall and you couldn't even tell there was another carpet under it. I just rolled it up when I left.
This is just an idea, but I hope you figure something out. Or maybe those foam like tile things that are designed for garages or children's indoor play areas. My husband has some of those in his workshop. They fit together like a puzzle, interlocking. I think he got them at Sam's. His are bright colors, like for a kid's room, but I have seen them in deep gray for garage floors.
Good luck finding a solution. A girl's gotta quilt, ya know!
Dina