If you're confident you can pull this job off, you can fill the gap with
plumbers epoxy putty. You can buy it at Home Depot or a hardware store. It comes in a small tube about 1" dia. x 4" long.
Once this stuff cures, it's as hard as steel. To use it, you break off a piece of putty a bit larger than the gap you need to fill. Knead the putty between your fingers to activate the epoxy.
Press the putty into the gap as far as you can. The putty will cure to 95% of its hardness within 15 minutes, so you only have about 5 minutes to shape the epoxy to match the contours of the horn. Once the gap is completely filled, smooth the surface with a 1" wide putty knife, flush with the top of the horn.
Let the epoxy cure overnight and you can sand the surface smooth to match the body contours. You can match the paint with some touch up laquer, found at most auto parts stores.
All that's left to do is re-drill the hole for your strap button screw. Make sure to drill into new wood or into the epoxy plug, not the gap between the two.
Any other suggestions?