Reporting back...My schedule pretty much limits me to weekends for working on this so progress is slow.
I couldn't figure out how to quote multiple replies in a single post so I'll just respond to each in turn.
DaytonaCharlie & Brad: The vacuum caps are secure and in place. The vacuum line to the petcock was intact and secure at both ends. The carb boots looked OK but I loosened and them and reset the carbs just to be sure.
Travis: Idle screw is OK; I dropped it on the right side.
Nickwiz: The gas flows freely in the 'prime' position and 'on' when vacuum is applied. I thought maybe the tank vent was plugged and that was keeping the gas from flowing but it's OK.
After checking all the above I started it again. No change.

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Then I noticed the exhaust note sounded like it was missing. I pulled all four plugs (checked OK) and ensured the high tension leads were secure to the plugs and coils.
Reassembled, tried again; no change.
Then I pulled the low voltage leads to the right coil (cylinders 2-3) while it was running; no change. Cylinders 2 and 3 weren't firing. Pulling the leads to left coil (1-4) killed the engine immediately.
I swapped the coils left to right (repositioned the plug leads), crimped the low voltage leads a little, and tried again. Now it runs almost OK.
The idle is a little ragged but it will continue running at 1100 rpm or so with no choke. At idle, the exhaust note sounds 'flat', like a Ducati, as if one cylinder is not firing. There is a *very* slight stumble, barely noticeable, immediately off idle when the throttle is blipped quickly. Once above idle, it runs smoothly and pulls well. A few runs up and down the street suggest it is running fine except for the questionable exhaust note. This bike is 100% stock so I'm not sure if that is how it's supposed to sound.
Right now it still has the original 2-3 coil firing cylinders 1-4, and vice versa. I'll just ride it and see how it feels.
One of the motorcycle writers -- can't remember which one -- once said "I've fixed a lot of carburetor problems with a new battery." So it goes.
Thanks to all,
Patrick Cherry
Ventura, CA