I've been reading the back post and I saw that someone wanted to restore wooden wheels. There were several responses but none where what I do.
I design furniture and craft custom pieces besides doing some restoration and decoy carving. A few years back, before I retired, I had a line made from rescued barn boards and beams. I called it, "Barn Boutique, A Step Above Shabby Chic". However, that's beside the point.
I restored old pieces, including a pair of my own 42" cannon wheels over 25 years ago and they have held-up fine in bad weather and rolling on streets during parades.
First, see if you can leave as much of the dozy, punky wood as possible for a base. Then squirt Elmer's Wood Stabilizer in and on the affected areas.
When ready, dampen the work and drizzle Elmer's ProBond Polyurethane into the problems. Have it fill all of the voids.
It will swell and expand into all cracks and crevices. After it dries you can cut/sand/shave what is beyond where you want it.
This works like Gorilla Glue but it should be considerably less expensive.
NO! You do NOT have to worry needlessly about it forcing the cracks to open more.
No! It will NOT fall out as the humidity expands and contracts the wood.
YES! It works (in my professional opinion) better and easier than Bondo.
Hub areas can be rebuilt successfuly with Durham's Water Putty".
I may use 19th c. hand tools but I do use chemicals that work too.
Been there; done that.
Richard "The Wood Butcher"
P.S.: Here's an after thought. Perhaps you might like to imitate this repair job?