overloading your alternator will lead to bigger costs in the long run (such as a burnt out alternator). The big 3 is a must. Also, make sure you have the right size power wires running from your existing battery to your amp. Upgrading the size of that wire will be of benefit as well.
Here's a quick analogy: you can't stuff 10lbs of shit into a 5lb bag. There are basically two things happening here. First thing is, your electrical system can't handle the demand. Second thing is (and I'm just assuming here, forgive me if I'm wrong about your setup) you're probably running 8 gauge power wire. The bigger the wire, the easier the flow (and higher the flow) during high demand. Even if you're running a stock battery/alternator I would still opt to run 1/0 from your battery to your amp (probably to a 1/0 distro block that accepts 4/8 guage out. That alone will offer an improvement.
Here's what bugs me about the "add a second battery" suggestions. You can add a second battery, but again, your alternator will have to work harder to keep both batteries charged. In the end, you're not benefiting much by adding a second battery if all you have is a 70amp alternator. Don't get me wrong, the benefit is there, but in my opinion it's not worth it. Now, if you had a 150amp or higher alternator, throw two extra batteries in that bitch.
And to address your headlight solution because of dimming, I'd be careful with that. Especially if you're running cheap ballasts.
I'm by no means an expert, but I've been through your position many times.