I tried that, but I'm not sure at which point it randomizes it. I tried about 30 seconds before the end and kept resetting and it was the same party over and over.

Either way, I have moved on now and got back my Bright Shield Rune. I'm trying to look on the positive side of now I get to use some different characters! There's a bit of dialogue with them so I got to see some new dialogue too. That's not so bad.