Blacksmith bolt/rivet supply has 3/16" diameter round head "rivets" out to 2" long. You can make a countersunk header and just beat down the round head for a tang bolt, or you can make a flat header and just pancake it out a bit for a larger diameter - there is a lot of meat to work with. At 3/16 shank, you can go #8 and remove some material, #10 or do coarse 3/16-24 which is actually fairly common on a lot of old guns.