just have to figure out how to power both amps with a rechargeable battery that can be charged via USB

Search for lithium battery charger. Here is one along with a video someone made about the device and how it works.

Here is what I was thinking of, but I didn't see a ready-made module on eBay.

 

Search for lithium battery charger. Here is one along with a video someone made about the device and how it works.

Here is what I was thinking of, but I didn't see a ready-made module on eBay.

I have that USB charger module, that maxintegrated power supply though seems perfect for what I'm doing and more. I'll have to consider that route.