Gregory's Server
The translator notices this and creates a new auth handle based on its idea of your effective uids/gids (see libfshelp/exec-reauth.c); and then the exec server gives the new task a fresh proc port. You cannot access the new task because of setuid/EXEC_SECURE, but as you created the executable you still control what it does.
@civodul
In particular it may send its proc/auth ports back to the original task, and the original proc port may then be recovered by a simple
proc_task2proc (other_proc, mach_task_self (), &my_proc)
The exact auth port I don't think can be recovered, but at least you now have another auth port with your effective uids/gids.
@janneke