If you go to another bank they will most likly tell you no. :( Each time you go to a bank and ask it dings your score on average two points. I looks like you took the higher intrest to rid the cosigner not a bad choise. however you will need to make payments for a few months. Also the dealer will pull your credit at many banks at one time. it is aganst the law for them to pull your credit score. they will get your score but they can not pull it once and then shop around. just look at you credit report after going to a dealer ship. these will stay on the report for three years. good thing is when you ask for money later they see that your report was pulled all at the same time so they know you were car shopping.
If it were me i'd wait a year, save money on the side and upgrade to the z28 next summer. thus building credit. that will lower you intrest in the future.
hope this helps good luck.
Ps I can't wait for my camaro 4 more weeks