..... Since you have done all the proper checks it seems to me to need a new card.
Heat must be significant due to the delay before the trouble pops up again.
Using the video card harder, seems to accelerate the fault, and you are satisfied that the card fan is 100%?
I am lucky never to have had any component suffer a slow death. Either they behave for me or they just stop.
It only takes one of the thousands of resistors to "go high" or an electrolytic to go open circuit and the rest follows.
Obviously you could try substitution, but it might be better to spend the time choosing a new video card.