I've had a similar problem with other hardware, my solution was to lower my expectations of "having a shop" to fix it.
No shop will want to have the expectations to successfully fix a complex GPU, unless it's their main business, as the solution can potentially not be 'reballing the memory modules' and they might just break your GPU in the process, they don't wanna have to pay you back in case they do, otherwise the risk they are undertaking isn't worth the chance of they fixing it and getting your X euros.
Go to hardware communities and ask them if they'd like to have a go at it, find somebody reputable and go with them.
Otherwise based on what you said, you literally will have to trash it, or find a way to constantly cool it down in a very reliable way (Good luck! I tried the same with a CPU with an overheating issue and failed miserably. Hopefully you'll manage it)
