I would seriously consider a 16 x 16 x 9.3 - 74R -- a serious rifle round, not far behind the .375 H & H.
Most good drillings are VERY carefully made to keep weight down (think thin barrels where they can be thin, safely). So, you may not have enough "meat" to permit choke tube installation.
If you do find something you like with fixed chokes, you can adjust pattern performance, more than many expect, by cartridge selection -- and even more by careful handloading. Moderate velocities (around 1200 fps), hard shot, then adding buffering, tighten and even out patterns considerably. Spreader wads or inserts, with the opposites, open chokes. Feasible changes are +- one full designation and often more.
