Another benefit to building an amp based off a single 12V rail is that you can use cheap sealed lead acid batteries to power it. These are VERY easy to charge, cheap, and available in many different sizes. They are pretty much small car batteries. Yes, they're heavy but that's the penalty for lots of capacity with older (but cheaper and easier to implement) technology. The batteries used in computer UPS systems or home alarm system backups would work perfectly. Just search amazon for "sealed lead acid" and you will find a ton of options.
Another thing I failed to mention is that you have to also be careful when discharging Li-Ion batteries. If you drain too much power from them you can damage the battery such that it will no longer take a charge. This means you either have to build a sophisticated power management system that keeps track of the current into and out of the battery and shuts your amp down when it thinks the battery is depleted, or you have to just try to play it safe. "playing it safe" is what RC helicopter/plane pilots do. They know how long they can typically fly on a fully charged battery so they set an egg timer and clip it to their controller. When the time is up they stop flying because continuing to do so may damage the battery.
Another thing I failed to mention is that you have to also be careful when discharging Li-Ion batteries. If you drain too much power from them you can damage the battery such that it will no longer take a charge. This means you either have to build a sophisticated power management system that keeps track of the current into and out of the battery and shuts your amp down when it thinks the battery is depleted, or you have to just try to play it safe. "playing it safe" is what RC helicopter/plane pilots do. They know how long they can typically fly on a fully charged battery so they set an egg timer and clip it to their controller. When the time is up they stop flying because continuing to do so may damage the battery.