With the symptoms you have described, it's just a matter of time until someone either forgets to fill the HST and fries the pump or the constant overheating causes contact surface failure of something - pump, seal or bearing. I think it's time to think about either doing some measureable diagnostics or tearing the HST unit down an finding out what's wrong with it.
Aside from having a runny nose & running a fever, does the HST function as it should? If yes, then it seems like a flow obstruction that is preventing circulating of the oil - not the primary flow that is providing power transfer, but the secondary flow that is lubricating and moving heat.
One thing that I'd want to check is if hydraulic fluid (oil) is actually circulating through the oil filter.
Can you get an IR thermometer reading from different parts of the HST as it warms up?
-Jim