Choosing from Audio Capacitor's, Batteries, HO alternator?

The only thing that will increase how long you can use your system while the car is off is batteries. Capacitors simply store and release energy they obtain from the vehicles charging system and are of little use when the vehicles engine is not running. You need to add a battery or batteries if you want to extend your play time when the engine is off. There are specialized batteries made by Kinetic and Stinger that have some insane amp ratings but they cost $$$. To obtain 1-2 hours with that system you will need a bank of at least 4 normal batteries you may just want to spend the $ on a Kinetic.