I haven't tried this yet, but I have a thought - perhaps if you used double-stick tape to attach the tyvek to a sheet of printer paper it would feed it through better. I live in cold country, and I think all the dry static would make the plastic statically charged which in turn would make it stick to the roller. Just a thought! HTH!
I know I'm a little late finding this... but, when you want to turn something inside out, like your handles, pin a big safety pin into one side of one end, then start pushing it through. The pin will give you something to push along. You could proably have both handles done in 5 min that way!