I know there are plenty of these guns out there that run reliably as is, but there are a lot that don't. Yours and mine are of the latter group.
Check out this thread:
Sooo I wanted another 308 rifle, and was pondering back and forth between going Aero, PSA, or buying something used off here. My financial priorities do not align with mid to high tier 308AR/AR10's so under $1500 but closer to $1000. This would not be precision focused and will wear a 1-4/1-6...
www.snipershide.com
I'm sure there are more on here.
You probably will never get the gun to work properly until you get that sub-standard recoil system fixed. The buffer's too light (probably ~3.8oz) and the spring is most likely too weak for a 308. Also check the length of your gas tube, possibly too short.
I went through basically the same thing just recently with my PSA 16" build. Faxon 16" pencil bbl. 0.750 gas journal with a 0.093" port. Adjustable gas block. Sticking with the original AR15 buffer tube, I installed a Kaw Valley Precision 5.6oz buffer (2.5" long to work in that buffer tube which has a 7" internal depth) and a Sprinco Orange buffer spring. This made it perform admirably without my suppressor. Soon as I installed my suppressor the problems started again and it was not reliable at all at any gas setting.
When I decided to go even heavier with the buffer, I found that I would have to go with the longer Armalite/Vltor-length buffer tube with a 7-5/8" internal depth. This allows the 308 to use a normal-length (3.25" long) buffer.
Here's the easy button for that:
https://www.eurooptic.com/Armalite-AR-10-6-POS-Receiver-EXT-Kit.aspx
That kit will come with a H3 AR15 carbine buffer, which weighs ~5.4oz. This may fix all your problems without going heavier.
I bought a different XH buffer with a 308 rifle spring from Heavybuffers.com which weighs 8.5oz.
This wound up slowing down the bolt too much and I started experimenting with different weights by mix/match swapping out of the internal weights until everything worked suppressed/unsuppressed. Finally settled on 2 tungsten weights and 1 steel weight in the XH buffer to get a weight of 7.6oz. It now runs smooth and reliable with very little recoil. I only have to make a simple adjustment to the gas block to go from unsuppressed to suppressed to duplicate the good performance. It was a long and frustrating road to get it all to work properly, some of it self-inflicted. YMMV