eysikal hasn't been around since they asked, so they've haven't read any of our answers.
At first when I was experimenting today I thought it was impossible to salvage, but now I might have a solution. Someone will have to test if it actually works in the actual glitched scenario. Take the winged Epoch to the Present, Middle Ages, or Prehistoric. Then use the time gates to get to the hangar.
This is the technical explanation. There's a variable, at $7F00CD in the SNES version, that's used for the various Epoch close-up scenes. Before getting the Epoch and when you return to the hangar using the wingless Epoch, it's set to 00. When you're departing to another time period from one of these scenes, it's set to 01. When the Epoch has been left at the End of Time, it's 06. There are other values from cutscenes too, but those are the ones that can easily produced multiple times in a playthrough. I couldn't find any location events after obtaining the flying Epoch that would set the variable back to 00 and not get immediately overridden by the warp-out, which is why I initially concluded it was impossible. The point of JLukas' advice, "before talking to Gaspar" is to move the Epoch from the hangar before that variable can be set again.
Because of the way the event code is set up, when you try to use the seats when $7F00CD is set to 01, it automatically tries to run the "warp out" sequence. Since you didn't get a chance to select an era from the era select, it fails to send you anywhere. So, we need to set the era (variable:$7E02AF) beforehand with the flying Epoch (luckily the variable doesn't get overriden during all that travel), but it has to be a map the wingless one can go to. So the Future and post-fall Dark Ages are out, and the End of Time too because it sets $7F00CD to another value the hangar can't deal with.
Edit:
Another possibility. If you haven't seen Lavos erupt yet, then use the Bucket, see the eruption, decline to fight, then use the gates to either get to Keeper's Dome, or if you parked it somewhere besides the End of Time, the Epoch. When the game returns from the scene of looking at Lavos, it sets 7F00CD to 02, same value it uses when you cancel out of the era select in one of the Epoch close-up scenes. But in this case, you have a chance to leave and preserve the value rather than it getting overwritten when the Epoch warps out.
