Is exhaust back pressure the culprit here?

The 360 in my son's car was starting, idling, and running well with the timing set with 3" exhaust pipes ending short of the rear axle so we could install a rear sway bar. Today, we had the remaining segments of pipes over the axle and the tips installed. Because of the tight fit between sway bar, axle, fuel tank, and frame rail, they reduced the pipe down to 2.25" the last bit and used our 2.25" A-body stainless tips. Stopped for lunch and when starting the car to leave, it wanted to bog and die, no more nice low idle. Had to play with it to keep it running. Same story when we made two other stops along the way home. All this seemingly following the trip to the exhaust shop.

The question becomes...did the pipe size reduction at the rear end create a back pressure in the exhaust which is now affecting the ignition timing? If so, what is the fix for this? Do we advance or retard the timing?