A bad ground wouldn't cause a low voltage at the coils.
The Dyna system has both coils drawing power almost all the time. They are shut off for a moment when the spark is triggered then back on pretty quickly.
So your coils are drawing a bit over 2 amps each (over 3 amps each if you have 3 ohm coils) or a bit less than 5 amps total through the black/white wire. I think the harness uses 1.25mm wire which will drop about 1 volt in 50 feet at 5 amps. I don't think there's 50 feet of wire between the battery and the coils.
You're measuring voltage to ground at the coil though: the battery voltage will sag with load current. Measure the actual voltage drop between the battery + terminal and the coil black/white wire under load. If you have much more than one volt I would try to isolate it, measure the drop across the keyswitch, kill switch, and main fuse. Those, and maybe 15 feet of wire, are all that's between the battery terminal and the coil connection.
Note that the coils will get pretty hot powered for a long time with no cooling air. The Dyna S should be no problem - the electronics survive being inside the engine cases - but a Dyna III black box might overheat with no air flow.
Adding a relay is pretty simple. Make sure you actually have a harness voltage drop and not just battery voltage sag before doing the relay!
Some progress to report:
I cleaned all connections related to the coil ignition last night, ran more tests. I was still getting 1.3-1.4V difference between the coil and the battery (One side of the voltmeter on the coil +, one side on the battery +). So I went about installing a relay. Took my time, made it nice and clean. Checked the voltage once installed, only a drop of about 0.1V. Excellent.
Cleaned four D8EA plugs, put them in, checked my timing was correct using only a timing light. Didn't check with the strobe. Looked like the following:
With the rotor turned (On the outside line):
T F
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With the rotor not turned (Right on the line):
T F
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According to Dyna, this is spot on.
Turned the carbs back to 1 turn each, went for a ride for about 30 minutes. The bike ran well except that now I've got a hesitation at around 5K. The bike backfires. Once it did that I backed off. I tried it again later in the ride and it did it again. I'm thinking lean at this point OR maybe too much advance? Is it possible that now that I have more fire, I'll need larger mains than 105s?
Checked the plugs when I got back. The 1&2 were decent, tan colored insulator but a little black here and there. Number three looked really good. Number 4 looked terrible. Completely carbon fouled. Keep in mind that I cleaned out the carbs AGAIN this weekend. I'm thinking I might have a bad cap or wire.
Question: Can I flip the wires between 1 and 4 to check if this is a cap/wire issue?
Thanks!