Calamity:
Civil war artillery wheels felloes were held in alignment by wrought iron dowels. Once a jig is worked up, this process is a good way to go. Later, when iron hubs were in common use and segmented felloes were still being used, one way to hold the felloes in alignment was by a wood key just like a Woodruff key. This is probably best for your wheels since the felloes are not weakened as much as with a metal dowel. A biscuit joiner would be ideal for cutting the slots and instead of a wood key you should use a metal key. Make sure the key is recessed below the top of the felloes so they do not interfere with putting on the tire. For a wheel the size you need, I would make the inside of the tire the same size as the outside of the wheel then heat the tire evenly and install. If you put a tire on a light wheel that is too tight it will compress everything too much and might cause you to say bad things. Remember, when putting the wheel together, make sure that everything is tight, especially make sure that the spokes are seated to the bottom of their mortises and the felloes are seated tightly on the spokes. If you do wind up with a loose tire just shorten it and try again.
You did an exceptional job on your gun and I expect that you will do nothing less than an exceptional job on the wheels.
Maxcaliber