[morzh]

>> By "shunting across" with the DMM, I take it you mean to have the resistor in series between the test lead and the point in the radio under test?

Well...shunt is by definition is in parallel to what it shunts.
If you shunt a coronary artery, you put a new vessel (a piece of a vein from your leg) in parallel to the clogged artery.
The very word "shunt" acquired its latest meaning in 19th century from railroad use meaning "directing around / redirecting".

The thing in series is called "ballast."

As for the tube tester, mine is Hickok 600A which is, along with 800, are not that different from 533.
As Dale said, these MCTT (mutual conductance tube testers) will not tell you the tube is good. For instance, they do not measure leakage. Which, in some cases, like a unity gain power stage, where everything is DC-coupled, (I personally fell victim to oone such case) is very important. But if the tube is bad bad, it will tell you. Inter-electrode shorts, open filament, no emission, gas inside, weak - you will have these data. And in most cases this is enough, at least to start with.