Before you go and replace your motherboard, I would suggest checking if its the connection on the LCD that has gone bad. It happened on my wife's 2009 MBP 13 inch and a replacement of the LCD fixed the issue (cost 100$ - DIY). My only suggestion is test it on another non-retina MBP (BTW - yours is not retina).
I can confirm that all parts from a 2010, 2011 and 2012 will fit without issue through all the years on the 15 inch A1286. I replaced the top case of a 2012 with a 2011 and swapped a 2010 with a 2012 (needed to change language layout US->UK) and everything fits fine (i.e. screw holes placements are exactly the same across all three years).
What I cannot confirm is if you can swap a motherboard from 2010 with 2012 and have all the connectors in the right places. My guess is that most of everything should be fine except for maybe the heatsink and bluetooth/wireless and the LCD cables possibly being shorter/longer (already mentioned).
Good luck.