I've never had this specific situation come up before, so just wanted to see if anyone else has seen it.

Right now I'm heading into next season with five open schollies. I have a junior who's almost certain to leave as an EE. However, I have another junior on the bench who's whining about playing time.

What order do those get determined in - i.e. if the whiner transfers, am I then safe from the other junior going EE (as I'll then be at the six open schollie cap)? Or will the EE leave first, and then have to worry about getting hit with the transfer?

There isn't a cap on the number of open scholarships - the 6 limit is the number of people in one class.  The limit for EEs only applies when you have players graduating - since it looks like your upcoming 5 openings are 3 Seniors and 2 walk-ons, you can lose 2 EEs.  I don't know this limits transfers or only EEs, but even if it does, since you have 2 walk-ons both Juniors could leave.