Yes, FRED does very much throw a fit about that. But the mission saves, and it works fine in game. Something I didn't mention is that with my first method, your ship doesn't show up in the "wingmen" box at all; Alpha 2, 3, and 4 are the only dots there, and in A1's spot, there is nothing.
A workaround is to not vaporize the real Alpha 1. Instead, make sure that Alpha wing doesn't have a hotkey (f5), and to make a sabotage-subsystem (hull) sexp that happens when the player ship is damaged to <50%. Now, as far as you could possibly tell, the player Alpha#p 1 is Alpha 1.
EDIT: Except, that any loadout you've selected for "Alpha 1" won't work, as far as I know. You would either have to use the custom wing names thing to add Alpha#p wing, or else make this a scamble mission.