There are several good examples of integral and non-integral suppression designs for shotguns. The ones employing barrel porting look like swiss cheese and not just for the last 12" or so, but the entire length. Do you not think that if putting a couple holes, for the last bit of barrel, would have worked that that's what they would have done? Also, a fair share of these are only 410 and 20gauge, not the larger 12 you're dealing with.
I'm not 100% sure, but there's about what, 12.5" of barrel in front of front sight?
If your intent is to cut holes in the barrel, why don't you just lop off 4" (legal >18") and put more suppressor off the muzzle? This is where your real gains will be.
I just think you're making for a very complex and involved design when an easier and more effective answer is available. Your gun, your stamp, your wishes. Carry on.