Does the rod have to be tapered so much? I mean, I know that some old original rods were very strongly tapered. But the real question is how much room is there down inside the ramrod hole at the point where the lock bolt passes through the web. if you are going to make a replacement, you might want to first push a larger rod down the hole (gently) and see what your limits are. It might be possible to make a new rod slightly larger, so as to keep it from being so fragile. 3/16 is pretty small diameter! I recently saw an antique that had an antique rod similarly tapered, down to about 3/16 like yours. And the rod practically wallowed around down in there, like a little boy wearing his daddy's boots.
As for making a new rod, if you want to make it yourself, you might see about getting a piece of hickory or ash, or even white oak flooring. Flooring companies often have culls that they just dispose of, so you don't have to buy a bundle of flooring to get one board. You can check the end grain to find a piece that is quarter sawn. On a quarter sawn board, it's fairly easy to draw a saw line that follows the grain (so that you don't have to split it). (I have split them, too, but sometimes the edges splinter and splinters can be hard to control. Sawing on the grain can get you to the same place but with a reduced risk of ruining the material.) Then round it up somewhat with rasps, but leave it oversize. It will be wavy, but that easy to fix by wrapping wet rags around the bent sections for a few hours. The rod will soak up some water, and then you can heat it gently with a torch or over a forge fire until it gets soft enough to straighten. When it cools it will stay straight. When it is straight as you can get it, let it dry for a few days, then you can finish rounding it and tapering it to finished proportions.
