A couple things to try...
First - what kind of needle are you using? I never knew it could make so much difference, but when I switched to a straw needle versus the thick one I was using, it was like sliding through butter. I think I have size 11 straw and size 10 sharps in my bag right now. And some undetermined really thick needles too.
Second - use some type of clip or pin to hold the next few inches of binding where you want it if you aren't already doing so - I ended up with a serious hand cramp from holding the binding so hard.
Third - test drive a few thimbles to see what you like. I'm finding that I probably need one on the thumb of my supporting hand along with the one on my middle finger as my thumbnail is scratched from catching the needle as it comes through.
Cheers, K