I looked at the mini to see if would be a better bet, as you say it covers a 2x2 in flower, that would bean 2 of them covers a 2x4 and your looking more like a 4x4 space, even though that's not exact, so you would need 4 of them, may get away with 3.
To be fair the nextlights look legit, there are so many dodgy LEDs these days, but they give good information on ppfd and coverage and look to be reasonable diodes not cheap shit. Its just the price point that bothers me. If you had a 5x5 I would say go for it because to cover that space for that price is not too bad. But 5x5 is 25 square feet and your looking to light up 12 square feet so that ppfd of 1400 would be 2800+ which is far too much and so intense given you cant raise your light in your 4 foot ceiling you would defo bleach your plants.
At the risk of coming across like a sales man (which I'm not) I have just purchased 2x 260w Quantum board kits(yet to receive since I'm in the uk) I bought them to cover one half of my 8x4 flower tent, which the will do very well. They are dimmable so you can lower the power as much as you like and they are about the most efficient LED tech out there, using really good diodes. They are also from one of the advertisers on here who spent a lot of time researching the tech and putting this together, there are more and more threads on here showing how they perform and on their website they have all the info on coverage and spectrum.
They are from
https://horticulturelightinggroup.com/products/260w-qb-led-kit
may say sold out but if you email them they may have some in stock. Defo worth emailing them, that's what I did.
The other benefit for you is the really low profile design so your losing less height from your limited space.
Here is the main thread
https://www.rollitup.org/t/diy-with-quantum-boards.927159/
They do sell fully pre made versions of their lights too, but the Kits are very very simple to put together, I hear its a 10 minute job.
Here is a good thread with a great example of what they can do
https://www.rollitup.org/t/quantum-boards-across-the-pond-in-the-uk.935279/
Anyway two of those would set you back $570 total. Which is a bloody big difference and incredibly high performance.
Right, now we have gone through that option we can talk about another option. 315cmh (ceramic metal halide)
A 315cmh has an amazing spectrum compared to HPS or MH lights, 315w puts out around the same as 500w of HPS because its more efficient and as I say the spectrum is far superior to hps. You could hang one vertically and position your plants around it or horizontal and have a ScrOG set up below it to keep all your plant/s very low profile.
I have a mate who after moving grows in a similar space, although he's probably pushing it about 4.5x4.5 ft so he has a bit more room but less height since his grow is in the side of a loft space and the ceilings slope. He still makes good use of his space and pulls some good weight off his narrow but tall plants which surround his vertical light.
Anyway, hope this is some help to you. You should check out the links above and ask questions to those who use both types of lighting. Feel free to ask me anything, I'm not the best person to answer though, there are folks far more enlightened than me. I can always point you to someone that knows more if I don't know an answer.