Mike: I know the source of the battery troubles, will bring that topic up in detail a little later. It's something I "treat" fairly often, like 1-2 times per year on bikes that come by. (Right now I am stuck in AR until Sunday or Monday.) It is rooted in the use for BOTH the 3-ohm Dyna coils and the Dyna S ignition on these bikes, which together draws so much power that the battery cannot "catch up" in charge until 4000 RPM. Over time, this damages, then destroys, the battery chemistry, and then the battery.
Not to be argumentative, but I've been running a Dyna S and 3 ohm coils in the 750 since 1990. I have yet to have a battery last less than 7 years.
Well, I hope this doesn't get too techie, as it has a lot of 'engineer-speak' in it...but it may help explain why this sometimes appears to be OK:
That performance is much more typical of the Dyna S units built before 2005 (which was when their current version(s) came out) most likely because their older Hall Effect triggers had Darlington transistor output inside, making their "ON" voltage drop about 1.2 volts (leaving the coils with [Battery volts - 1.2 volts] as their charge supply): this lowers the total current used. The early ones seemed to last much longer than the ones we have seen since then, too. The last (post-2005) Dyna S that I tested for this output voltage drop (just before the customer removed it and threw it away) measured a scant 0.40v drop, which means their outputs are likely being switched with a second-stage, single-junction transistor (much like in my units) so as to increase the current available to the coils. The newer ones then show a charge voltage available of: [Battery voltage - 0.40v], a difference of [1.2-0.4=] +0.8 volts. With 3 ohm coils, this becomes a current increase to the alternator of 0.8/3= 0.267 amp extra per coil, or nearly (0.8x[2x.267])= 0.427 amp extra on the whole system (where 0.8 = the 80% dwell time of these units).
So, after all that gobbledeegook...what it comes to is this: if the Dyna S is made with their 'new' parts, it uses even more power (over 0.4 amp extra) than they used to, which was already quite a bit.
The [very] few 750s I have seen that got along with the Dyna combination of 3 ohm coils and Dyna S triggers have always (every one) been hiway-ridden bikes, not city or commuter bikes. This makes perfect sense: if the bike is ridden more at speeds over 4000 RPM most of the time, it will 'keep up' with the Dyna parts' demands (even this K6 made the trip across the USA with little trouble). But, if ridden in typical Eastern (or even Denver, CO) city traffic, they have not, in my experience, ever 'lived' with the combination. They could take either the 3-ohm coils or the Dyna S triggers separately and survive, but the combination always put the battery under heavy current loads and frequent low-charge stints (which slowly damages the plates and chemistry). A perfect example of this showed up on my driveway last August: the beautiful, original Antares Red 750F1 in town (owned by the Denver Museum's Curator) suddenly started having low-battery issues. He brought the bike by after completing one of my favorite rides: west out of Denver on I-70 to Glenwood Springs, south thru Aspen over Independence Pass, back thru Buena Vista to hiway 285, then down into Denver (about 300+ miles). The last 30-ish miles of this becomes 30-40 MPH downhill traffic in the summertime tourist season, the rest is open hiway (and the rider said he 'idled' it down the long hill, in the upper gears, at lower engine RPM). The bike had always sported the 3.0 ohm coils since he bought it (8 years ago, I think) just fine, but he installed a Dyna S himself (because I told him I wouldn't do it with those coils) before he took this trip: the battery would not electric start the bike when he got home from the ride, nor on my driveway. It read 11.8 volts until the key turned on, then just 9.8 volts. It was (is) a top-flight, maintenance-free, Yuasa battery only 1 year old. He came by to get a Resistor Pack in 1.5 ohms, decided to make it 2.0 ohms instead, and installed it that weekend. It fixed things right up for him again. So, he effectively replaced the coils with 5-ohm coils so he could get his battery charged up again: that's very typical of what I see happen over and over. The last bike I 'fixed' like this (2 weeks ago) is the K8 I just finished refurbishing: it had 3.0 ohm coils on it, and was parked some 15 years ago for the owner getting tired of "issues" (it had a battery-charge connector hanging under the left side cover, as testimony to electrical troubles being one of those - and a relay feeding those hungry coils, to make it all worse). After installing normal coils, it has been fine again. For racing, these coils with relay feeds make sense: for street, not so much?