Yes, it should be a rather quick change. I use to do so before the element tab was changed. Used my alt when my other supports didn't have a light eidolon which I would just change my alt to Phoenix.

For AutoCrimson's issue, I find it weird that your friends see Diabolos when you say you have Apocalypse set up, unless you mean as a sub eidolon, cause you sub eidolons don't matter. Or unless you literally went straight to using team set B and left Diabolos on A...