We have our mattress on the floor too (dd is 7.5 months and a clumsy crawler at best). However, our bedrooms are upstairs and now that winter is here those rooms are a bit chilly during the day, even if I could stay up there with her while she napped.
Our solution was to build her a "nest" in the living room, near her toy area. We put down a soft mat, then topped that with a small woven rug (she likes the texture, and cotton rag rugs can withstand almost anything a baby can dish out), and finally an overstuffed boppy-style pillow. When she falls asleep we tuck her over/around/into the boppy (her head rests on top of one of the boppy "arms" while her bottom sits down in the open center area) and put her favorite stuffed toy next to her. Since she's right there in the living room I can check on her frequently and I can hear her when she wakes up.
It might not work if you have other little children or large pets running around, but the "baby nest" works great for us and may help you too!