Get a PSA lower. Doesn't matter what Gen it will fit. That upper will not fit anyone else's lower that is known. Their take down pins are also different. I have 2 PSA's . A rifle and pistol in 308. I built the pistol and the only parts that are PSA are the upper and lower receivers.
I have 2 308 pistols w/12.5" barrels I will post a pic or two when I get home I think the rails are 10". 308s do not have an inside voice. Torch that off indoors w/o ear pro and you won't be hearing anything for a long while.
This will work. If you don't like this stock you can order just the buffer tube, buffer and spring and install a fixed stock from somewhere else.
https://www.armalite.com/SACItem.aspx?Item=EA6050