When shifting the transmission into reverse it feels like something is binding up?

With this many miles I would suspect the rear end needs to be rebuilt or the transmission is going out. But I have also seen the rear brake shoes catch in reverse as well. Let's start by removing the rear wheels to look at the brake shoes/pads. If they look okay remove the drive shaft and try to turn the drive shaft yoke by hand to see if you feel grinding while turning it backwards. If that feels okay let's remove the transmission pan to look for metal shavings which is a sign the transmission is going bad. Please let me know what you find and upload images or videos if you find the problem or have any questions.