Incidentally, I believe that what you call 'checking to see if it is sleep mode' is really the empeg starting up linux, the kernel, and the player so that when/if you decide to use it, there is an instant startup time like a traditional car stereo, rather than a 10 second wait while linux starts.
I guess it switches on the display to show that it's working, so that people don't think it's doing nothing when they get in the car first thing - visual feedback.
If you were feeling like some soldering, I'm sure you could
make a simple circuit that you insert in the amp remote line that doesn't give a signal out to the amp until it's received a signal in from the empeg for, say, 10 seconds. Would mean you couldn't listen to the empeg until 10 seconds have elapsed when you want to use it, but should prevent the issue you're having now.
I'm sure someone more proficient at electronics than I could knock up a simple circuit - I'm almost certain it's a very simple thing to do - probably using a 555 timer or similar - but I wouldn't have a clue of how to draw it
HTH,
A.