I am undertaking the same project (you may have seen the same topics in a different thread). I ran into the stair height issue as well, and the code is so tight that it is almost unavoidable if you are putting down anything on the floor. Here is what my inspector allowed me to do. I am extending the bottom step out about three feet (all the way to the wall) and creating a large landing area. The landing area will step down to the floor in a drop that will be only about 5 inches (compared to 8" stair rise), but because the landing area breaks up the stair pattern, giving a visual queue that something is changing, he said it was acceptable. I am, in fact, going to start building this tonight.
I put down 1" XPS, no poly, and put OSB over it. I would estimate that the total job took me about 45 - 60 minutes per sheet of OSB, which included putting down insulation, taping, cutting the plywood, drilling lots of holes in concrete, etc. Not fun work, but nothing tricky about it either.