Great thread. I'm from the school of "If it isn't broken- etc" on pitch, and am lucky in that any field grade M12 Winchester with factory stock made from 1936 through 1960 will fit me "near perfect" for field and casual clays shooting. Trap, Skeet, SC and perhaps Live birds, another scenario for gun fit perhaps. So the answers of- No recoil, if you can hit birds cosistently, etc- ring true. And i am also about 90% a serious waterfowler for all seasons- the early warm Sept. nuisance geese, through flight birds into oct-Nov, ending early Dec. and then the late Jan-Feb season for Geese. That might mean the LOP that worked for Sept. shirtsleeves early Goose hunting on a golf course "poop prize patrol" squad, well you get the drift.
Having done beaucoup steel fabrication work, as well as being a proficient rough-in and finish carpenter, I can say that even with new "production" homes, roughed in in a Midwest late Spring- many builders are loath to hang in the pre-fit exterior doors until later on. Why? because wood shrinks and expands with internal moisture (even treated wood) and the heat of summer and conversely, with the cold of winter. Another example is in finish work, with crown moulding- not all intersecting walls are a true 45% to make a perfect 90%, and you often have to make a "jig tracing" to get a tight, gap free mitered joint--Point is, the door jamb test is a 'field fix" by either the protractor method tends to be more consistent in accuracy.
refering to Jack O'Connor's "The Shotgun Book" Knopf 1965--page 159-he has the outline of a sidelocked DT side-by and dimensions detailed alphabetically- as he shows: "If measurements G (LOP from front trigger to heel of stock) and H (LOP from front trigger to toe of stock) are given, the pitch will be right" I assume he may have mean those measurements as given by the purchaser or the purchaser and a gun fitter with a try gun- just my guess.
Jack also details pitch further on pages 160 and 161. Just for fun, I took my Smith 12 3E with 28" barrels and my Smith Grade 2 with 30" barrels (both have identical stock dims, both made aprox 1908) and after verifying with a framing square and 6 ft. level I had a plumbed to a 90% intersecting door jamb to insure "accuracy" and there is about 3/4" pitch at muzzles difference between those two on the 2" OAL barrel length- Truth be told, there could be any amount of difference between the two and it wouldn't matter at all, as I kill pheasants cleanly over dogs with either one of those 12 bores.
Sometimes, and this is just one old guy's opinion here, perhaps we "over-think" the details, but then, I am apparently an easy person to fit in a shotgun, I can't say. Feathers in the air and a heft to the game strap (within the limit of course) are, to me, the ultimate criteria. I also only shoot 12 bores, so I may have more possible pattern 'forgiveness"!!