Just get a cheap PC UPS. PC UPSs are just that, battery+inverter in a nice package and I think cheaper than buying them separate. Plus they include the electronics which know when to stop charging the battery.
Here's what works with powering lasers (or video projectors) outdoors:
1) PC PSUs. I have a beefy one and no problem powering 1W laser for 4 hours. Though even it says it can't handle more than 900W out. PSUs have batteries and inverters inside them, which leads to option 2
2) Most 12V rechargeable batteries + an inverter which can handle the load. A 10000 mAh battery I tried once powered a 1.4W laser I had for hours.
3) Your car (your cars battery) + inverter
4) Generators which use fuels. These are good for several reasons:
1. no need to waste time recharging
2. no need to worry of battery life, just get enough fuel with you
But have disadvantages too:
1. Are a bit noisy. I tried a Honda one once. If there's music playing, forget about this, not a problem then. if a quiet, more "artistic" or cultural scenario, it might be annoying to the crowd. Maybe go with other options or get a long power cable and move it far enough so the sound won't bother people.
2. They generate a bit of gas. May or may not be an issue for you.
Ideally, if you make your own laser projectors and need to use them outdoor a lot in places with no close power source (for whatever reason), maybe you should put a rechargeable battery inside the projector itself. Think about it, at least for my projectors most stuff inside have a 12V PSU which converts mains power to 12VDC. It seems a waste to convert a 12V DC from a battery to 110/220V AC which is going to be converted to 12V DC inside the projector anyway.
BTW, why is pure sine wave stressed out so much here? I haven't had issues with the cheapest chinese inverters. Don't the AC to DC PSUs inside the projector handle that themselves?