I've shot a LOT through Double Bull mesh with numerous different b-heads. In fact, we had a fairly extensive test and actually hung the shoot through mesh over our tuning frame and shot several different brands of b-heads through mesh up to 30 and 40 yards. Following and totally agreeing with Double Bulls suggestions, we found that the Rocket mech b-heads with straight blade tips shot the best. For this reason, I insist on shooting Rocket Slammerhead 90's (1 3/4" cut) and Rocket Steelheads (1 1/4" cut)for my Gobbler hunting when forced to shoot through window mesh. For instances that the windows are open I then use a slightly larger cutting head that features the L-type blade tips like the 2" Rocket Hammerhead. It's been my experience that there simply is NOT a better choice for a Turkey b-head than a large cutting mech b-head.
Slammerhead 90
Hammerhead 100
Regarding shotguns through the mesh, don't worry about it at all. I hosted a few diffenent hunters last year from my Double Bull Matrix and they took 4 different longbeards from my blind with 12 gauges..... without lifting or rolling up the netting. I would personally not advise it though,simply because the shotgun blast melts and tearsaway about a softball sized hole in the mesh! It neveraltered the shot one bit because all Gobblers were stoned in their tracks! LOL! I would still prefer to use the mesh in all case however. It just minimizes the chance of a silent bird sneaking in and busting you. Even the slightest bit of movement when the suns angle is wrong through a window can spook the wariest of Tom. I'll take every advantage I can get and it simlpy allows a hunter to move around comfortably. Good luck and good huntin this Spring.