I've used a sample of vinyl carpet. I liked it, but I think you will find it to hard based on what you write.
A piece of advice though: before you do the work pour some hot water on the material to see how it behaves when you will wash you hakama. No reason to put something in there that will fall apart if you decide to get rid of the tatami dirt and sweat that builds up in the fabric
Good day to all
JJ