Chosen Solution
First of all the original problem points to the NVIDIA issue and should be covered by a extended 4 year after purchase warranty by Apple. The geniuses should know about that. The only thing with your new board i can think of, as you seem to have checked everything obvious, is the DC in connection under the LB. Hope you didn’t get a fishy board.
I had the same problem. But I found a very simple solution. I hooked up my back up drive to my macbook pro and while starting I kept pressing the option button. Both start up option appeared the screen and I opted for back up drive option. Then through disk utility I repaired my macbook pro’s hard drive and installed a clean copy from my back up drive. It took me about 45 minutes only. Now my macbook pro boots up very fast and it works as usually amazingly !