Can I stay in the parking lot after the aquarium closes to have a late dinner at der beirgarden, after visiting the aquarium, and not have an issue with leaving the parking garage after hours?

There is floors u will explore to park. Park ur car then go and buy it tikets and then as u exit u will see a tikets machine and u pay for them there and when u drive out they scan it to make sure u payed

The more direct question I tried to ask is, what time do I have to leave the garage by?

Parking is 15 dollars and you must re-scan your parking ticket in order to exit. Georgia Aquarium parking passes are valid ONLY for the Georgia Aquarium parking deck. So therefore you won't be able to leave your car.