Note that the original TIROS satellites weren't geostationary orbiters, just polar orbiters. The orientation of the satellite is such that leads me to believe you are seeing an image from one of the geostationary orbiters.

But, there is one thing that leads me to wonder if it isn't even a newer storm than Allen (which I could buy except for one thing, noted below). The only geostationary satellite in orbit taking images over the Atlantic/EPac at the time was GOES-2 (as an aside, it still functions for data transmissions, but hasn't been used for imagery for many years), and it was positioned over 60°W.

This satellite appears to be positioned over 75°W, where the newer GOES-EAST satellites are located. GOES-5 was the first satellite to be located at this spot, and it wasn't launched until 1981. Allen, of course, was a 1980 storm. I think it's an image from GOES-5, GOES-8, or GOES-12...likely the first...but the when part? I'm not sure on that. I can't pin down any storm that would fit between 1980 and 1995. Note that the EPac twin to the Gulf storm matches if it is Allen, however -- Isis was a storm of minimal hurricane intensity around the time Allen was in that location.