Have you tried using it on a bench flat? Or broken it in with some lather and a bottle to help break it's back, this may help the creases, I have also then rubbed Nivea vitamin E cream into it and rubbing again with the bottle when dried again helped a lot with my English bridle.

My roo travel strop I made is very flexible, but mainly because it is only 0.8mm ( 1/32" ) thick does work nice also but.