Strange Panel layout! Not that it affects the electricity. Who is the manufacturer of the panel?

When you shut the audio breaker off did anything else go off? If nothing else went off, you already have a dedicated circuit.

The lights dimming when you turn the amp on is caused by a voltage drop. When anything is turned on, typically, is when largest amount of electricity is used. Do the lights dim when the refrigerator starts? The light circuit and the fridge circuit are on the same phase, while the audio circuit is on the "other" phase.

Take your meter and set it to voltage. Check the voltage between the two main feeds. Then check the voltage from each one of the feeds to ground. Then check the voltage from each one of the feeds to the neutral,(this should be the same reading as the feed to ground).

I'll PM you with my e-mail address for the photos. Jim