What's this?

An
active restoration project thread that has gone nearly a month without a post? Heresy!
I'm scratching my head along with you on the HV issue but I can at least provide one facepalm-worthy suggestion to another annoyance you're having... Put the test CRT in "upside down" so the anode connection is on the other side and the HV lead runs across the top. The test CRT is small enough to probably allow the HV lead to still reach, and then the weird spring on the HV lead won't put up so much of a fight. There appears to be enough slack on the socket wiring to rotate 180 degrees without issue.
Continuing this thought-process, consider the possibility that the damned spring is sapping the HV through cracks in the very much vintage rubber HV lead insulation? That would explain the low HV measurement even with the tube disconnected. I'd bypass the whole HV lead assembly with a modern replacement and see if anything improves. There's no hidden resistor in series up under the suction-cup either, right? You've checked the filament current limiting resistors up under the HV rectifier, too? Swap the rectifier out for a string of microwave oven rectifier diodes? Aside from the flyback and doorknob cap, the HV lead is one of a rapidly dwindling list of things you haven't yet substituted for known or presumed working parts...
Going further down the grasping-at-straws path, pop an analog milliamp-meter in series with the HV supply directly after the rectifier and see if there's more current than expected being drawn. Obviously only a floating analog meter will work here. I'm sure someone makes a digital meter capable of measuring 0-100mA up around the 15kV zone, but it probably comes with a hefty price tag, and it sure isn't something you're going to use very often anyway.
Even further down the "Nothing makes any sense, why doesn't it just work!" path:
Is your chicken blood fresh, or are you using that freeze-dried just add water stuff they sell to the wannabe-wiccans? Perhaps the bleached skulls need more dribbly candle wax on them, or maybe they need less. Swirl your tea-leaves in the opposite direction next time... Try everything! (In moderation.)