You can drop your party in the roster and then shuffle the order (after swapping items).

Tested and it works.

Hey! Switching the characters within the team (dragging them to another team slot will move the items also) should switch up the starting order also. In some maps the spawn order might be reversed, but they should still take turns according to the order within the team. Could you check again if the starting order really stays the same when mixing up the team? If so, it is a bug and I will look into it.

I was just going to note what Redbeak said. Swapping character pics move equipment with them. Much faster than roster swapping.

Oh, didnt know it works that way. I think it’s worth pointing that out in the tutorial since I wouldnt know I have to drag portraits otherwise