I put a 5.56 AR together for a friend with a CBC upper on a PSA lower, seems to shoot good, no issues. Build quality seems to be on par with PSA.
I have several uppers & lowers from PSA in .300bo, 7.62x39 and 9mm. The only issue I ever had was with a PSA 'premium' BCG. It seemed to drag in a .300bo PSA 8" upper and wouldn't reliably cycle subsonic. But that same BCG ran fine in a PSA 16" .300bo upper. The 8" upper got a lightweight AIM BCG which ran fine.
As for gas system, most 16" .300bo uppers are gonna be pistol length systems, that seems to run best with both sub & supersonic ammo. there are a few carbine length systems but I'm betting none of them will be in your price range.
I also have an RF 10" upper in 7.62x39 w/AIM BCG. Mine's had no issues, still torqued properly. I think RF's quality control gotten better but from what I've read PSA & CBC have better customer service if there's issues.