I would just run the 770/990 from your 15 amp circuit. I am going to assume that since you live in an apartment, you can not play your system at levels anywhere close to the power output levels you could get from your 770. If you have a problem with the circuit breaker tripping, then see the next paragraph.

There is no reason too that you can not use your 20 amp circuit in the kitchen as well. Just use an extension cord that has 12 gauge conductors. The only issue you might have though is if you are using your system and you use the microwave or some other high current appliance that is on the same kitchen circuit.