You need to tune the gas. That's pretty much a given for a 308 even without a suppressor; adding a suppressor definitely made your rifle overgassed, no question about it.
Seems like you got a lot of other input sending you different directions, but this is pretty simple and commonly known - 308 ARs almost always need gas tuning.
You should expect to use different tuning settings for suppressed vs unsuppressed, and probably different settings for mil-surp vs commercial 308 depending on the load and how sensitive you are to the rifle's function. Some sort of switchable gas block is convenient for that. The Seekins block looks pretty good although I've only used their $60 adjustable model and not the switchable model so far.