The narrower aspect ratio worked, and I got the hole size for press fitting the filaments just about perfect.

The filaments definitely had a left or right twist to them depending on which end I inserted first.  I tried to balance that out later on, but the first 20 or so were just randomly oriented.

<EDIT> My son and I played catch with these by bouncing them off the ground and they survived with no consequences.  They are pretty bouncy!  I believe this means I have sufficient depth at the insertion point of the filaments to keep them there with just the press-fit.</EDIT>

Now to model the transmission for it again.

However, I just thought of an alternative to string trimmer filament which might actually work better..

Zip-ties!

Bend them into a loop and they don't deflect very much from the cylinder shape side to side, but they still flex nicely along the circumference of the cylinder for better performance as a tire as well.

They won't have quite as much grip as the triangular trimmer line, but I honestly think the flexing off axis is going to be more of an issue.  I already had to make one design compromise based on that.

The flat shape also lends itself much better to being woven into a cross hatch pattern for a Mars rover style tire, which was the original intention of this project before the Mecanum prospect took over.

I'm going to have to try them later.