The Iver Johnson line of doubles included some features which well known makes didn't like chopper-lump barrels.
In addition to the basic Hercules, I.J. made two clay target specific doubles, the well known and popular SKEET-ER which are seen fairly often with dealers asking userous prices.
And, the much less known and seldom found Iver Johnson SUPERTRAP.
Wenig would probably be the best bet for a reasonable priced new stock for your gun. In
The Double Gun Journal, Volume Nineteen, Issue 4, Colin McLagan has a nice article on the SKEET-ER which shows an engraved gun. Other then that gun, I've not seen any references to Iver Johnson regularly offering engraved guns.