I was looking at this guy's inexpensive DIY project with a low-cost monolight.
Super Easy DIY Rechargeable Battery Power Pack For Event Photographers - DIY Photography
I'm not really any type of expert on inverters, but I thought there were basically three grades of inverters, those being low cost cheapies or "square" current models,better, yet still noisy
modified sine wave models, and then at the top of the pyramid
pure sine wave inverters. I own a Tronix Explorer pure sine wave inverter that uses a pretty heavy 12-volt, 12-ampere-hour battery that weighs about 8 or 9 pounds I guess (last one was an Enercell 2301219 model), and the whole unit as a whole has been good for 9 years, in that time using up the original battery, then one replacement I installed, and then in late 2015, I had to put Battery #3 into it.
12volt, 12 amp has been PLENTY powerful and fast for me, running mostly 1 x 400 W-s power pack or 1x 600 Watt-s off of it, but It has also run my 1600 W-s pack as well, and the 2400 W-s on occasion; it might take 25-30 second to charge all the capacitors in the 2400 Black Line, but I've fired 60 to 100 frames that way, but you have to "make them count".
I dunno...I bought it to power a 2400 W-s power pack on "occasional use" jobs, and it's sloooooow with the big pack on it, but with a 200- or 400-Watt Speedotron Brown line pack, it's almost as fast as 110-volt wall current. it was said to only be able to handle 1200 W-s, but it can do more, only pretty slowly. I think for a smaller, 150-300 W-s monolight like the Neewers, that the smaller, 7-volt battery would have adequate power, and still light weight; the above DIY setup looks good.
I think if you got a "decent"
modified sine wave inverter, and not some $25 car repair place cheapie inverter, that you'd likely be okay: I've looked at the Neewer C300 units on-line...they've been made basically unchanged since at least 2010, and they don't look like they have any digital controls...not trying to belittle them, but they look like they are likely build on old-school, low-tech platforms...the way my Speedotron gear is: 1970's technology...