On a trap gun, you don't need to carry the ramrod with you. Leave it back at the loading bench. I don't know any trap club that lets you stand and load the gun at the firing line.
Even if you do take it into the field to hunt, you can carry the stick down the middle of your back, under the possible's bag strap, with the jag stuck under your belt. It won't move, or get in the way of any shoulder or hand movement, but is available by simply reaching behind your neck, and pulling the rod up and out, over your shoulder.
If you insist on having the ramrod with the gun, you can either run it along the off side of the forestock, or drill a hole under the barrel, and install one, or more pipes attached to half rib pieces soldered to the barrel. You do not need to install a solid half rib under the barrel, unless you want to. The barrel supports the pipes and ramrod. The jag will extend past the muzzle, because of the location of the nipple into the barrel, but not by much. Remember, the nipple enters the barrel just in front of the breechplug face, with maybe 1/8" between the two to give some room for crud to build up while shooting before it begins to interfere with ignition.