I can't answer your question about the safety of the mattress but I am one who had success in transitioning a not-quite 20-month-old to a twin bed. We didn't put the mattress on the floor, but we bought a bed from IKEA that was very low to the ground. We had no problem at all, much to my surprise. I am sure this had something to do with the fact that we did this when we moved, and it was his first room--previously his crib was in our bedroom but he actually co-slept with us. It also helped that his best buddy had a twin bed also, so DS saw his friend's "big boy" bed and wanted the same thing.

HTH even a little...