Serial number always helps get better guesses and opinions.
Has anyone pulled the battery out and cleaned all the corrosion that builds up under the battery and replaced any power cables and connectors that seem to be soaked in corrosion ?
How clean is the the battery, both in a housekeeping manner, and in the 'electrical shorts to frame' manner?
I would also want to know if they checked the battery at rest AND under hydraulic stall load to see if it is good. (what were the numbers of the results)
Next, I would have the directional contacts replaced (as a complete assembly, not just the tips), since you say, "forward acts as expected", and the only differences between forward and reverse are in the contactors control of the electron flow direction.