Thanks for sending me the save file. I figured out the bug, and it will be fixed in version 0.9.22.
If you have a save prior to that one (ideally, one that was taken before the party AND the training before the one that triggered the party), I'd recommend going back to it. You can in theory use the travel sphere to escape, as you mentioned before, and it won't break much, however if you do that I recommend avoiding the twins training until you get the fixed version, as the bug resets the progress on that path and can loop endlessly as long as you continue training with the twins (you can always escape with the travel sphere again, but that doesn't seem ideal, of course).
I think you should be able to simply replay through the path, but if some other problem arises, you can tell me what it is, and I'll fix your save file, worst case scenario.