One option you might consider, since you're concerned about adjusting your sights too much, and are clearly dual purposing your shotty...

Since your Gobble Dots are barrel mounted (both sights ride the vent rib), you have the option of adding a recevier mount, like a B-Square Saddle Mount, and mounting a different sight/scope.

I use the same Benelli Supernova for Turkey and Coyotes, for coyotes, I have a B-square with a Tru-Glo red dot sight installed, for turkeys, I have TruGlo Tru Point Xtreme fiber-O sights mounted on the vent rib for turkeys. I used 2 part auto epoxy to "bed" the saddle mount to the receiver (took a couple tries, couldn't get the mount off the first time!) so it's consistent every time I install it. It was PRETTY close without the epoxy as long as I sort of "seated" the mount rearward, and torqued the screws the same each time. Two screws, a choke, and some ammo, and I can swap from a turkey call to a coyote call LITERALLY in under 5min.

Another option, of course, would be to buy a 2nd barrel and use barrel mounted sights on both, but it's a LOT more expensive to do it this way ($150-200 bucks for a new barrel, $20 for a B-square saddle mount).