Congrats on your new to you ZR1 and welcome to the Registry.
Pretty much everyone who owns a ZR1 has been where you are today. I'd consider having the Bose system repaired. The place many of us has used is Dr Dons:
http://www.doctordons.com/corvetteradios.htm
The factory system is not bad when working properly and you may find you like the LT-5 music so much you don't even use the radio much. I'll bet you'll find the cost of Dr Dons service to be very reasonable and fast. I'd also leave a little budget available for a few of the other known issues you're likely to face. If they haven't already been replaced you can count on needed a set of injectors.
Enjoy and good luck. Post some before and after pics!