All of these 2011 AMD based systems are JUNK. They fail the same way the NVIDIA 8600 did in 2007/2008, just they took longer to fail. My fume extractor gets good and busy inhaling smoke from all the dead HD 6750M I am replacing everyday in my office.
You can fit an 820-2849 In there, BUT it is a downgrade in CPU. It is this downgrade in CPU power that actually saves you. The 820-2849 has a dual core CPU compared to your 820-2914 board's quad core, which produces less heat. Do keep in mind that this dual core CPU board has the SAME COOLING SYSTEM AS YOUR QUAD CORE CPU BOARD because Apple is clueless when it comes to proper thermal design.
The 820-2849 also has a GPU that is NOT a piece of crap like the 820-2914's HD6750M that will not keep failing. Keep in mind that the combination of crap AMD HD 6750M GPU + quad core sandy bridge processor is what is killing that GPU to begin with. Even if the HD 6750M wasn't junk, it is paired with one of the hottest running mobile processors of the past five years which will kill it just by sharing a heatsink with the GPU.
You already have a bad GPU and a bad cooling design. Put a QUAD core sandy bridge processor of the 820-2914 board you have in that system, instead of the DUAL CORE processor of the 820-2849 board in there, and you have a recipe for disaster. What Apple was thinking when they made this is beyond me, but it definitely wasn't that you would have a working machine 3 years from your purchase date.
The right thing to do is to keep killing it within the 90 days by running GPUtest & furmark until they give you a retina for free. It works, and is what they deserve for taking $2000+ of your money and giving you this pile of junk. Be kind and courteous to them while insisting that this canot keep happening because you use the laptop for work. They do not have classic unibodies to give you as replacements, so they will replace it with a retina which is a far better and more reliable machine.
If you want to mess with putting a different board in there, you can put an 820-2849 and it will be fine. It does not share any of the lvds_mux issues or the kernel panicing because of dropping VRAM pgood signals of the 820-2850. But in this case, you are paying for a downgrade.
The right thing to do here is to keep killing it natrually and keep bringing it back to Apple until they give you a retina.