A more serious idea - very labor intensive, but this is rec.woodworking

.... so I googled chair mat, and found a couple wood offerings on the
first half of the first results page. Brookstone has bamboo ones, and
there are others he
http://www.bestpriceseating.com/bewochmaintw.html
Or just get a 4x8 sheet of nice oak-veneer ply, and finish it like you
would a wood floor.
I'm not sure how to increase rolling resistance, other than possibly a
clear rubber or soft plastic mat on top of the wood one, which should
slow things down a little.
If it were me, I'd probably suck it up and get a tacky plastic one -
there are so many available (google) that there should be some that
might be less tacky?
Andy