It's problematic to establish a solid bite on carbon dropouts without tearing them apart. (one good argument against non-metal dropouts). So, I don't think the OP will ever get enough bite to hold fast against chain tension. That's why it's critical that the top forward axle position (on both sides, but certainly on the right) provides perfect wheel centering.

If the wheel has to be canted back off the forward face of the right dropout, the chain tension will always pull it back forward, which is what the OP is reporting. As I said, it's either a wheel dish or rear triangle problem, (third time's the charm?) and needs to be properly diagnosed and fixed. I don't know which, nor how new or old the frame is, so I hesitate to advise further except to see a dealer who actually knows what he's doing.