Case Nutty’s advise is sound.
I have had the rear plate off my 1370 its not that hard to do if you have a cherry picker/engine crane.
I’m with case nutty, repair the front cylinders first then proceed to the 3Pt problem by eliminating any possible linkage problem first.
P.S> You said that some times the tractor will not shift into reverse.
If the pressure for the filter is not in the green area on the gauge before you start shifting sometimes you will get gear grind.
How is your filter pressure?
A filter and Oil change hopefully will fix your problem.
But Please consider doing what Case nutty suggests first and fix some of your problems.
If you do pull the rear plate, take the time to clean out the area real good before you re-install the rear plate.