Help - Can't figure out way to connect spool to webbing

[GeeTwo]

Have you considered using an appropriate piece of timing belt, cut down to the circumference of the sheave, then rivet your webbing onto it in such a way that the webbing both holds the ends of the belt fragment together, and grips the webbing for the lift?

Another alternative might be to use a high-strength flexible adhesive (gorilla glue or shoe goo) to do the same thing.

Or, of course, both...

Edit: and yes, Mike's suggestion of larger flanges is definitely in order!

2nd edit: as you can 3-d print a spool, a totally different solution would be to 3-d print a spool that accepts a COTS metal hub with some bolts, then engages with the webbing, and provides the needed flanges.