OK, after a whirlwind of a week, I was able to look into the connections on my Cyclone, and here's what I found:
Main GI connector on power board had already been repinned by previous owner to trifurcon pins. Headers looked good, but I reflowed the solder anyway.
PF GI relay board had been burned. It was hacked around with a wire soldered to the back of the board, etc. Not pretty, but electrically sound. I undid the hack and repinned.
Backbox GI relay looked OK, but I repinned it anyway.
Seems the backbox GI goes through the interconnection board, and one of those had been burned and was already repinned, again with trifurcon and good looking headers. Other one looked OK, so I didn't mess with it at the moment.
So what I'm getting at is that the connections all look pretty good.
I went through and checked for losses. I found, like Swainer, some "parasitic losses:" of 0.1 volts here and there with all the fuses and relays. They do add up a bit.
But what was most interesting was that I can eliminate sections of the GI at a time (right PF, left PF, backbox coaster, backbox name), and none of them are a smoking gun, meaning that no single one of them are really dragging the voltage down. I really think it's a cumulative effect of the load, and perhaps an undersized winding on the transformer. Just not enough VA in that winding to keep the voltage up for all those bulbs. Heck, even with only half of them, they're still not all that bright.
I might look into a "sidecar" transformer just for the GI. I'd have to do a little math and see what I can find, but I built tube amps in another life, so I know there are 6.3V heater transformers to be had out there, I'm just not sure of the current capacities at the moment.
Thanks for listening and I'm still open to suggestions.