... I’m looking for advice on testing procedures for valves other than triodes ...
I’d like to avoid hunting for a valve tester ...
It seems like you need, "An easy way to test multiple types of valves, with quick reconfiguration between valve-type, and an easy-to-interpret indication of whether the valve is serviceable."
That's literally a description of a valve tester. So it seems wise to look into buying a service-grade valve tester. Those things were purpose-made for the TV repairman to take to the customer's home to test their TV valves.
... I expect there’d be at least as much effort in getting the tester working and calibrated as there would be in testing the valves
You don't need "calibrated" but rather, "
Which ones are dead, which ones are still kicking." This grade of tester was a few-hundred-quid 2 decades ago, and is still a few-hundred-quid today (are the enthusiasts dwindling faster than the testers?).
Or skip testing altogether and try the valve once the theremin is built. If it doesn't work, buy a new, tested valve from a vendor.
There's not really an easy way to
cheaply make a tester capable of testing a wide variety of valves that undercuts simply buying a working 1950s or 1960s valve tester. Pursuing that "inexpensive home-brew valve tester" will likely spend the money you thought was saved in buying the 1960s TV rather than purchasing just the parts required to construct a theremin (such is the challenge of salvage).