There's a lot to be said for having a rig that fits for standers... unfortunately, it tends to fight how you'd setup for sitters... kneeling is somewhere in between. One of the common problems is having a deep fore-end, which forces the forearm out and removes it's support of the gun. Another is gun balance, butt position, length, and scope distance.
The problem is that different shooters bias their rigs to their own preference, as the ideal means changing quite a lot on the rig, even the scope position. And because of this, shooters develop their own coping mechanisms... or not as the case may be, for each position... which means that the ideal might not be what you see, but what they can get away with.
I know one AA that sets his rig up for standing and copes with what it lacks for sitting, i go the other way around, some setup for a not perfect for all, some adjust as much as they can.
If you want, see if someone can take a pic of you from the side, so we can see the shoulders, and people may be able to help out
Normally wobbles = bad position, which can be for a variety of reasons.
I did have a rig where i'd solved a lot of the compromise problems, but it isn't suitable for everyone, and it's now being used by someone else now
... but working with a shooter recently made me aware that sometimes the setup isn't ideal, and it's a case of working out what can be shaved off one position and given to another. The more refined and specific something becomes, the less flexible it is for other situations.