It's not a very good idea to loosen all the strings without putting a brace behind the trem itself, because of the exact reason that happened to you, it will fall into the cavity.
If you are going to be playing exclusively in Eb, I would take it to a tech and have him set it up for Eb. That's the bad things about trems, you can't really alter tunings that easily.
So get it to a tech and have him set up the action, truss rod, and intonation for you.
My 2c.
Sometimes I hit notes only dogs can hear.