Interesting dilmena...lights still dim?
I'm not going to talk trash about any of your equipment but I've seen kids with the same problem switch out an amp and the problem is resolved. The reason a high quality amp may not suffer these issues is that they have all the capacitance needed built into them already. It's all about designing balanced hardware. Some lower end(even name brand) amp lines try to skimp on build parts. Manufacturer's generally use one amp design across as many markets as possible.
A quick fix in these situations can actually be the use of a capacitor. The problem isn't that you don't have enough available power it's just that batteries are not designed for a high draw of current in short time spans but capacitors are.
