That is your solution. They don't make a adapter for your hub. Go to a machine shop and have them fab one. More expensive than a new rear wheel. Try to make some kind of shim to work. Probably not going to work, but you might invent something to work. Use the rag joint. Not what you wanted. Everything has to be tight tolerances on the hub adapter. You have a unique problem to solve that can be done, but buying parts that actually fit together is the smart way to approach it. Then if you trash the rear wheel you simply buy a commonly found new one instead of looking all over hell for a 5/8" rear hub to fit your custom adapter.That would mean replacing the wheel. I need a solution!
When you say vintage Schwinn and it's 5/8ths" shank diameter is it possibly the older, high flange, Schwinn labeled Shimano LeTour hub? Because you can use the hub's high flange to directly bolt your sprocket to and it's so easy...I have a vintage Schwinn that I want to put a sprocket adpter on but the hub is 5/8" and the smallest adapter is 1". Any ideas?