Just on the odd chance that someone might find it useful, I'm tossing
out a couple of observations about Titebond III.

Making wagon wheels, FWIW (not asking for advice on that, the wheels are
as done as they're going to get and I know pretty much what I did wrong
and what I need to do in the future).

First, clamping the hub pieces together I used a couple of pieces of
3/4" melamine covered particleboard (the Home Despot stuff) and a half
inch bolt. That worked a treat for clamping but the first time I did it
I neglected to wax the melamine and was surprised to find that the hub
was bonded to it tightly enough to pull some wood fibers off. There
were a couple of drips of Titebond that just came off with my thumbnail,
but where it had been under clamping pressure I had to carve it off with
a chisel.

Second, had the wheels in the car for a couple of days. They had been
sitting in the shop for a week with all joints fitting tightly. After
sitting in the car for a couple of days one of the rims opened a gap at
one of the joints between the felloes (the pieces of the rim--it's in
four sections on these wheels, on larger ones it would have been in 6 or
more). I suspect that the heat did the Titebond in.

So, lessons about Titebond III:

(1) There are circumstances under which it sticks surprisingly well to
melamine--if you don't want it to do that be sure to wax (reminder--it
also sticks to steel--wax your clamps).

(2) Heat may soften Titebond III enough for a joint with residual
tension to open up.

Lessons about wheels:

There's a reason they put steel tires on them and it wasn't just because
they wear longer--before I do more wheels I really have to set up to
make and attach tires.