I just went to the TronicsFix store to check on the washer kit and you are correct. The kit on sale says that it will not work for the Slim.
Sorry about the error on my part.
I still think the issue is APU heat causing you problems.
One way to verify that would be to blow a lot more air on the heat sink using a blow dryer on cool (or cold spray), to see if you can get it to last longer than it goes now. The idea here is to get the problem to move.
That would show that the error is caused by heat. If that is so, then you are probably hosed. A reball by a professional might work, but that again would probably be temporary.
If it the upgrade does not get further along, then the problem is probably elsewhere.