Otto -
The NYC and PRR interchanged at Himrods Jct on the Fall Brook. Sometime during the steam age, the roads made an interline agreement, where NYC and PRR crews and power would run between Southport Yard in Elmira and Dewitt. It made for a more efficient interchange operation, because neither railroad had to wait for the other at Himrods. That continued up to Penn Central, and even then the crew districts had the interline agreement until the rosters were combined. NYC and PRR crews, IIRC, equalized mileage on a monthly basis.
I remember seeing the Southporter at Corning and Lyons in 1965, with PRR power and caboose (oops, "cabin car").
I suspect that the reason for the speed restriction on Track 4 on Bridge 636 at Seneca River was because of close clearance. The bridge was built in 1924, so the NYC standard design load would have certainly accommodated an M-1a with no speed restriction. A railroad wants at least six inches clearance to run trains at normal speed, but can go down to two inches or less at 10 mph, account rocking and rolling at higher speeds. Some steam locomotives "waddled" at certain speeds, and the M-1a could well have displayed that behavior. That probably also accounted for the overall division 30 mph speed restriction, because the NYC had closer track center spacing than most other eastern railroads.