As soon as you write the cheque, and drive the car around the block, the deal is done. Next time, drive the car around the block first. Note issues, have the salesperson/dealership sign and copy the list and then leave. That would be great if you could find all the problems by driving around the block the first time. So, my practice has been to write in a clause to give you a 30 day conditional issue fix/repair on all problems. They usually go for it. They won't go for it after the cheque.
On to your problem today. Being hard on the dealer gives them no interest in working quickly or at all on your problem. Be nice (that might be hard to do) and always put things in writing and ask for the copy of the service statement/report each time you take the car in and pick it up.
Keeping the paper work really helps.
Did you get a warranty of any kind regarding your purchase? Review your purchase agreement. Check for time frame of warranty if any?
Remember you did buy an older corvette and they do have more issues over time. Work on the angle that you are not happy with this purchase currently and request that you correct some of the issues. A legal letter might be required, but starts with "pulling out there guns". A letter from you with documentation is better from you. Do the paper work. You might be surprised how this gets things done. (or started in the right direction) Your only positon of strength now is , "I'm not a happy guy right now". "I just bought this car and it's got lots of problems!!!" "Please help me, I just bought this car!"