Not an 'even pay for amp repair'. They should be liable for it too as it was caused by the situation that they are at fault. If it would have burnt your car down or caused a wreck due to it being on fire while you're driving the shop could probably be sued for the damages as well. They should also for SURE be liable for the battery as well as the amp. The owner might have been cool with it, but if they are going to charge people to install electrical and other things, they should be ready to pay for damages because of a shitty install. You have before and after pictures, you have everything you need. Be polite and ask them to replace it all. If they refuse, take them to court for the amp, battery, and court cost.
Dont take the kinetic either...they shouldnt be able to fuck you on a nice piece of equipment and then make you downgrade because its convenient for them.