If case life is good and you are sure pressure is low, then yes perhaps it is time to start exploring limitations within other variables.
I see you have a brake so you probably don't have a whip problem. It is true that the M700 is truly at its limit when laoded to full RUM velocities. I think Dan Lilja got right up this one a while back via an article on his site.
In my .375RUM, I am able to run a 225 grain Bullet at 3250fps, producing one hole groups at 100 yards (a fairly stout barrel). I can shoot a 260 grain bullet at 3120fps for around .75". On some days, if I get scared of all of that recoil, I shoot all to hell. The M700 is (in theory) at its absolute limits of stress/ load bearing athese velocities.
Hand holds, trigger let off, grip tension- all have an immensely profound effect on groupings at the power level your are using so start by observing your own practices in order to eliminate these variables. Then again, recoil may be so light due to an effective muzzle brake
, as to not suffer from the effects of hand hold position and tension. You will have to observe this for yourself. Is there a high level of recoil? If so, it is likely that hand hold tension/position will be a major factor in accuracy.
Another variable is pinching within the bedding platform. Check it over and watch for tight areas around the recoil lug (am assuming the rifle is bedded).
Changes in hand loads will produce yet another set of variables.
Anyway, those would be the three areas I would look into if I was determined to load the cartridge balls to the walls- assuming you are correct in your initial observations regarding current pressures (everyone gets caught out with pressure problems atleast a few times in their reloading careers).
As for bridging, I don't think it is a problem in this instance but am so glad somebody is willing to bring the subject up. Not enough people understand the ramifications of powder bridging in the big Magnum cartridges. RoyinIdaho brought up a serious and real issue that occurs from time time and needs to be shared on the boards as he has done in order to warn others.