There is tons of 12v stuff out there. Use a 12v power amp. battery pre amp pedals and your regular passive PA speakers. Avoid inverters, without proper grounds, they can be dangerous....PS, Maybe a hybrid system. Run a small inverter to power your board, everyone plugs into the board.. Run the board into a 12v amp for the heavy lifting. Much less power loss due to DC-AC-DC conversion
What you may be missing is high-powered 12V car power amps use inverters to step the voltage up. So I don't think there really is any way around the DC-AC-DC conversion if you want significant power.
Also, a big car stereo amp pulls a lot of current. I have a 5-channel Kicker KX700.5 amp in my truck that requires a 90A fuse. Power output with a 13.8V supply is 75W at 2 ohms x 4 and 400W at 2 ohms x 1 for the sub. The sub amp is class D which is supposed to be more efficient, but if you run this system at about 1/4 volume for 10 minutes it will drain the battery so far that the truck won't start.
Still, I have considered a stereo class D car amp such as a Kicker KXA400.2 and a battery-powered mixer like the Behringer Xenyx 1002B with a couple of hefty deep cycle batteries. I.E. use one side of the amp for mains, and one side for monitors.
Concerns:
1. My KX700.5 is supposed to run as long as the voltage remains between 9-16V. I am not a battery expert, but I think even a deep cycle battery will not last long if repeatedly discharged it to 9V.
2. As I mentioned previously, my KX700.5 can drain regular truck battery pretty fast. I think it would be necessary to operate the system conservatively for extended play time.
Battery powered amps I would consider:
1. Roland Cube Street EX
2. Roland BA-330
3. Soundboks
The Cube Street EX is very portable and is about the minimum volume I would consider for busking with bass. It's not very loud. Don't even bother with the regular Cube Street or Bass Cube RX as they are unusable IMHO.
Roland - CUBE Street EX | Battery-Powered Stereo Amplifier
The BA-330 actually makes less power that the Cube Street EX but I believe it holds together it bit better because it has 4 x 6.5 inch woofers versus 2 x 8 inch for the Cube Street EX. It's also about twice as big and heavy.
Roland - BA-330 | Stereo Portable Amplifier
I believe you can daisy chain a mix of the two Rolands and they both run of AA batteries. Buy a bunch of Eneloops and chargers.
I believe the Soundboks is way louder and way more expensive as well at $999. Running a few off a Xenyz 1002B would probably work pretty well. The Xenyx runs of three 9v batteries. I believe the Soundboks uses a lithium ion battery and includes a charger. You can buy extra batteries. [Invalid or Expired Link Removed] currently shows "out of stock"
behringer Product
If you really want clean and relatively loud, I think a small inverter type generator is really the best solution. I don't totally buy the argument that batteries are cleaner, as battery waste is extremely toxic. Also, some sort of fuel must be use somewhere to generate the energy that is used to charge the battery.
I am personally torn between the Cube Street EX, BA-330 and Jackery 240
Explorer 240 Portable Power Station
The Cube Street EX is the lightest and most convenient. The BA-330 would be hassle to carry if much walking is involved but it's noticeable louder. I think I could use the Jackery conservativelywith one of my existing amps and blow both of the Rolands away. I don't need any of them.
If you are interested, I linked videos for some of these amps in this post:
Roland MICRO CUBE RX Bass Combo Amp