My most recent turkey gun is a Browning Cynergy Ultimate Turkey that solves the cheek weld issue by having an adjustable comb height.  Unsure why other companies don't offer that option as I find it ideal.  I know there are several aftermarket options, like I mentioned above the GodaGrip Shotgun Wedge works great.
The milled-out receivers on some of the new Mossberg's are a step in the right direction. I also have a 940 Pro that comes milled and a Holosun Red Dot from the factory.  No trouble with cheek weld with it.
Ridge Rooster