I think I'm lucky - I love hand work and sewing the binding to the back means the quilt is almost ready to give away and I can get on with the next project! (although, I must admit that by the time I get halfway through a king size binding, I feel like it will last forever.)
One thing that helps with hand fatigue is pressing the bindings with steam, first away from the quilt, then the fold to the back side. I tried using glue a couple of times and that stuff is really great as long as you keep it away from where you need to sew. No need to pin and takes a LOT of stress off of your hands while you're sewing.
But, just pressing without glue works great for me, too. The crease seems to last long enough to get the binding sewn on and I'm not fighting with pins or clips - I can just sew and concentrate on keeping the stitches invisible.
Wearing a thimble does take practice and I think deemail is right about trying to use too large a thimble. Mine almost cut off the circulation in my fingertips, but they stay on. And they've also got a rim around the top and ridges along the sides so that the needle doesn't slide off the top. The whole thimble can catch the needle and push it - even along the sides.
Good luck to you and I hope you find something that makes this step more fun or rewarding for you!