The question that I have for you, is how electronically inclined are you??
I had this issue on my '94 Ultra, my neighbor on his '96... I traced it down to a drop in the engagement wire from the bars to the starter.. (Starter V should have been = to Batt V; it was 7v, not 12v!) That wasn't enought to engage the starter. This is why the Cap button (prior to me) works so well! I fixed it in a different way!
I took a relay, and captured the starting button to the coil; then to ground.. The switched side I went from Batt -> relay common, and partial to starter engagement. Using the pin numbers it went somethign like this
85 Starter button from Bars
30 12V (Batt)
87 Starter engagement
This has saved my butt since I installed it; that is after I rebuilt the old starter, and then replaced it and 2 batteries. This has been on the bike for about 6 years, never had an issue since!
I'll take pics when I get home of the install! Feel free to PM me with questions!