No, mate. Haven't got three weeks spare time....
Seriously, I'm familiar with the concept. It also affected various CARC models, even if the specific cause and cure wasn't exactly the same.
I want to see for myself exactly where the Volts are going missing, but the knowledge that the power supply to the starter solenoid is marginal from the factory is in the front of my mind.
Yes, that is true. By the way, with "searching" I meant "testing".
On general principles, changing the battery first would be the right thing to do, no question. It is almost 100% certainly past its use by date.
Why I might do some testing with it:
I might try and charge it, and see if it takes a charge at all, and if it does, how long it holds it and how much power it can really deliver. Probably none. That is just curiosity a the behaviour of a dying battery.
I would prefer to be not using a brand new battery for a long period of time for testing, possibly with multiple activations of the starter. If the old one can limp through that, I'd rather use it.
That is not intended as advice for anyone else, or an argument against changing a battery that is known to be bad, or even just suspect. New battery is the way to go. However, although I am not an electrician, I understand what the multimeter is telling me (mostly...), and enough about the basics to draw usable conclusions even from a half flat battery. The dead battery, in the worst case, perhaps wont be enough to turn the starter, but it will suffice to show me high resistance contacts, for instance.