Obviously I won't be able to see this, but still interested in your situation. Assuming you have the B&R rig and the upper and lower shrouds terminate aft of the mast. Also assuming then that pulling on the shroud, as you say, causes the entire mast to twist - i.e. pulling aft from one spreader and the other not tight enough to resist the torquing motion. So, seems this is still a function of rig TUNING, primarily shroud tension.
Again, I'm just thinking out loud, so don't put too much stock in this. Just trying to figure it out along with you. Do you have just one set of lower shrouds? And, do they terminate at the same chainplate as the upper shrouds? Assuming, also, that this is a double spreader rig with intermediate shrouds. ???