Maybe you might want to look into a Dahon single ( 20 inch wheels) non current production. If you want a 135 mm rear triangle get a 20 inch yeah 6 speed. The dropouts on mine are horizontal . I saw one on e bay a month ago for 120 dollars or so plus shipping.

You could have two wheels one for fix one free. I do not know the availability of flip flop hubs in 135 mm.