I bought a 7/8-20 panel nut that fit in the wheel and allowed the pulling bolts to be inserted on each side of it. I then took an impact socket and put it over the horn button wire. I used my puller to push on that socket. The hardest part was getting over my fear of breaking something. I cranked it down and left it for a day or two. Then I finally just cranked hard on it and it just came off like it was no big deal.
The shaft is tapered but no splines, just a key. Interesting.
Thanks to everyone for all the help and suggestions!