I have an Axis Heavy Barrel in 308. It is a right hand action. I shoot left handed.

I'd like a Boyd's stock. The thumbhole is out because of my crossed-up configuration. I looked at the standard monte carlo style, and would prefer not to have that big cheek weld bump on the wrong side.
Other than the tacticool (which I assume is one of their heavier stocks), what other styles do they have that are more cross-hand friendly? I'd like something lighter, as I do plan to do some hunting with this rifle.

TIA