You might have gotten an industrial treadle belt instead of the domestic.
Jenny at sew-classic.com will have the right one. You will need to cut off the end that doesn't have the clip in it. Stretch the belt across your shoulders really hard to get most of the initial stretch out of it and you won't have to keep cutting little bits out of it.
If you have a drill and a tiny little drill bit, it will make quick work of making a new hole for the clip (a heavy staple)
You could also drive a small gauge brad or finishing nail through the belt to make the hole. Put the belt on a block of scrap wood to keep from drilling or nailing into something you don't want to drill or nail into. :)
If you have some C-clamps, thread the belt through the handwheel area and clip one end up close to the front of the handwheel. Thread the other end through the cabinet, around the wheel, through the release loop and up through the cabinet. Put another clamp near the surface of the desk.
Now you can measure your belt and cut the free end, drill it and fit it and get the staple into it without losing the ends of the belt.
If you put a couple of inches of heat shrink insulation onto the belt before you attach the staple and close it, you can shrink it over the top of the clamp and eliminate that little clink-clink noise as the staple runs through the handwheel.
The belt doesn't need to be nearly as tight as you think. The machine will be much easier to treadle if the belt has more play in it than you think it could possibly need. I learned that only after I'd already put new belts on several treadles. :D
Have fun!