I have two OSS and two Thunderbeast suppressors and I've shot them on 7 different guns without having any accuracy issues. The POI did shift significantly after putting the suppressor on a couple of the guns. All the guns shoot just as well with the suppressor on.

Is it possible that the scope is the issue?

Is it possible that a screw connecting the stock to the rifle is loose?

Have you tried the suppressor on a different gun?

How does the gun group with just just the QD break when the suppressor isn't on?