I've responded to a few posts with this problem and I think I've started my own thread. I have a 1995 FXSTC that has done the click since probably 1996 as far as I remember. I think I have it fixed then a little time goes by and click, click, click. I have literally replaced everything in my starter system and have done what you just suggested. I've also replaced a starter that didn't need to be replaced. I even posted to a thread the advice you gave.
As simple and almost idiodic as it sounds, my bike seems to do this when it has sat for a week or so and the battery loses some power. I say this because it never (that I remember) does this on a new(er) battery. But after the battery is about a year old, click, click, click. If I put it on a charger for an hour or two, it fires up every time. But as soon as the bike sits a few days to a week, click, click, click.
I know I didn't give you anything you probably already didn't try or know, but that's all I've got. If you come up with something else be sure to post it. It's almost a challenge to me now to see who can come up with something original. Good luck.