Joel -- good work on resolving the steering issue, especially given the limited facilities available to you. And (yes, I'll go ahead and say it) kudos for excellent customer support by Vintage in proactively taking corrective action, without even being asked.
Regarding getting out the horn button: The other day I replaced the battery in wife's cell phone. The battery 'kit' came with a suction cup to aid in pulling off the back case and then the battery itself. I was surprised how much suction-power I could apply in the process of pulling the glued pieces apart.
I can't say the idea will work for your horn button (the curved button face might negate the effectiveness of the concave suction cup). But it seems that if you can get a suction cup to stick, you could exert some outward pull on the button while gently 'rocking' it with plastic prying tools.
PS: My wife's phone problem has been resolved with a new phone. I wasn't the battery. But the process of giving these shaky old hands a fine dexterity test reminded me: These are really shaky old hands.