I do not own a double, but I have found many two-piece stocked rifles to be finicky off the bench, including lever guns of all sorts and Lee-Enfields. The same applies to many full-length-bedded, one-piece-stocked rifles where any upward or downward pressure on the forestock is transmitted to the barrel.

Beleg, you can "kill two birds with one stone" by doing your shooting from the sitting position on the ground, with elbows rested on knees. This position is very steady and we actually finish-zero our hunting rifles from this position as even a one-piece-stocked, free-floated barrel rifle often hits a different POI when handheld.

It takes practice if you haven't spent time at it, but in every case I've tried, the strange effects of bench-shooting 2-piece-stocked rifles disappears with this method.

If you have no experience with it, start from 25m with a .22 or 15m with a good air rifle. Grip the rifle very firmly with the support hand. Over time you will feel new muscles used and little by little settle comfortable into the position.

I see many fellows on this Forum seem to zero their doubles on a 50m range, and if that is what you want to do you will find this sitting method to be very easy effective to rough and finish zero your rifle at that range. We shoot 50, 100, 150 and 200 meters to check zero all the way out.

I say "two birds" because one of the advantages of the sitting position is that it is field-useful, unlike the bench rest technique that really is a discipline of its own. Many bench shooting skills are not applicable to field shooting unless you do your hunting from a Hochsitz, etc.