RNR replied that our early 2011 motherboards were 6750M-only. They could not put 6770Ms on them. He did not offer to refund the extra we paid for the 6770M chips. He did say that they used the latest versions of the 6750M chips that have better cooling. eBay deletes your messages after a few months, so I no longer have a record of what we asked and were answered a year and a half ago.Note: He does good work, but he's not much of a conversationalist! :-)
I guess yours was a slightly later revision logic board than ours are, so yours could take the 6770M. Hope all of our replacements hold up until we can get decent new MacBooks.