Yeah, I've got the same "problem" and I've been thinking about fixing it for quite a while. My "fix" at the moment is to simply turn my key all the way back to off before starting the engine, so the empeg turns off and then back on again.
What you need to do is do some experimenting. I suspect the culprit is that your car's constant power is cut when the starter is engaged. This could be fixed by running a seperate constant power lead to the battery.
To check if it's just your amp, try connecting a small wire from constant power to the amp remote input on your amp. Then while your amp is forced on, try starting the engine while the empeg is playing.
Matthew