....stock without checkering could bring the date closer to 1770?
Per Neal and Back, stocks were checkered in 1770's. The early checkering style has much larger checkers than on the gun you posted. The fine checkering came into vogue in the 1780's and 90's. Almost all of the high end guns were checkered after 1770, but prior to that, most seem to have been without checkering.
Neal and Back list 32 fowlers built between 1760 and 1794. 28 have flat locks, only 4 have a round faced lock. One of the round faced locks is from 1764. the others are from 1776-1778.
Great British Gun Makers 1740-1790 would help you out a lot. It's fairly expensive, but it's cheaper than a barrel. Considering the time and money you will put into your gun, it's a bargain.