My test with another user connected to another session gives me some hope. I just need to find a way to isolate one of the launchers on the same windows session.
This part manages to confuse me.
So you should have Epic Account 1, named EP1 with it's own library on lets say C:\Epic1 and obviously its own email address.
On this account you should have a working Elite, paired with a frontier account named EP1Ed1
And another Epic Account 2, named EP2, again with it's own library in C:\Epic2, a email address different from the one used for the first Epic account, also with Elite paired with a different frontier account named EP2Ed2
So you start Epic launcher, signed in user is EP1, start Elite launcher, then start the game. Elite launcher closes by itself, Then you need to sign out the Epic launcher then exit the launcher. First Elite should still be running at this point.
Then start Epic launcher, sign in as EP2, start Elite launcher, start the game - at this point you say you get an error that Elite is already running?