3. Please permit me to respond here, gentlemen....
I am just about 100% sure this was not Braniff International operating an all-coach configured B727-200 as I cannot recall the original BN ever operating single class jet equipment. Their initial BAC One-Eleven aircraft even had a first class section in addition to coach as some of you may recall I flew in F on board the airplane with Braniff. BN did operate nonstop IAH-ACA service at one point with F/Y configured B727-200 aircraft.
So perhaps this was actually Eastern as I do believe they may have operated IAH-ACA nonstop for a brief time back in the early 1980's. And perhaps this was back when EA was operating A300 aircraft on weekday LGA-BOS Air-Shuttle flights thus freeing up an all-coach configured B727-200 which had been previously flown on LGA-BOS Air-Shuttle service and would appear again after the A300 was apparently found to be a bit too large for the route. If so, buckeyefanflyer may well be correct with this EA flight actually being operated on a LGA-IAH-ACA round trip routing.