I teach heavy support-hand thumb pressure onto the frame, and significantly further forward than most. I don't think you were applying too much lateral pressure, as you describe things; quite the contrary.
If you're deviating shots towards the support side in the absence of support-hand thumb pressure, were I you I would re-proof my trigger-finger relief; most likely looking at getting a little bit less finger on the trigger and rotating the entire shooting hand clockwise around the grip sufficient to achieve that goal.
Disengaging one or both thumbs has not proofed out well in my observation, and usually allows the weapon to roll or turn within the shooting grip both as the trigger is pressed and while recoil is happening; but your mileage may vary.