As a rebuttal to your rebuttal..lol I did not say to buy an MoCo branded battery...but it brings up a good point.
There are many batteries out there to choose from and many opinions on which is best. At my dealership, we only sold a few though: Bikemaster branded(Biker's Choice), Yuasa, and MoCo branded batteries which we bought from a HD dealer. Most batteries have a one year warranty, some cheaper have 6 months, some high end Bikemaster and Yuasa have a two year warranty. The MoCo batteries have a two year warranty.
That all being said...For customers, I would only install AGM or gel batteries of those three brands I mentioned(we've all seen what battery acid does to stuff and I did not want to be liable). I made three times the money to sell a non MoCo branded battery, but always recommended MoCo batteries first and my personal bikes I only use MoCo branded batteries...for many reasons:
I have seen HD batteries consistently last 5-6 yrs with the use of a battery tender..and only a few off brands do the same.
And if I develop a battery issue when I'm traveling, there is a huge network of HD dealers out there can warranty my battery easily. The other brands can be warranty replaced as well, but its tough to find your particular battery on the shelf of a motorcycle shop, and there would be waiting time to order it in.
I really try to give the MoCo the least money I can, but this is one case where I believe their product is the best choice.

Back to trouble shooting...The voltage drop is normal when the started is engaged..it is pulling from the battery. I really recommend grabbing a couple beers and switching batteries with a buddy that is not experiencing problems. Ride it a couple days and then you'll have an answer to your battery issue. The switch will take you half hour at most and all speculation is over. Once you have decided if its a battery issue or not, you can move to next step...yes you could have a starter issue, but always rule out the most common issues first...I've sold a couple thousand batteries, but only needed to fix a handful of starters.
No matter what you find, I cannot stress the importance of using a battery tender enough. The security bikes eat batteries, and use of the tender really can get you 5 yrs out of your new battery(whether you have security system or not)

Good luck bud, and let us know what you find.

 

I have a manual button on my Glide's starter solenoid, came in handy this summer when some kind of problem developed, obviously in the wiring or starter switch, since it starts fine with the manual button (actually just a bolt that pushed the contacts together). But the bike acts like yours most of the time now, starter clunks but won't turn over with the switch. Haven't tried to fix it yet, plans are to have the bike in pieces in the living room this winter, just go through the wiring then.

If the problem is a voltage drop from wiring or a switch, a new, more powerful battery might overcome it for a while, but the problem will probably come back. Seems to be a fairly common problem, lot of weak starter threads here (and the starter usually isn't the problem). Now that I've experienced getting the bike home under it's own power only because of that manual solenoid button/bolt, I'd want that on any big twin I might get. It's still wired so it won't turn over without the ignition on.

edit: And I just noticed how old this thread is... my bad, OP probably fixed this a long time ago.