I would suggest you do this:
1) Cut the traces for the Cathode grounds.
2) Solder in 2 x 1 OHM resistors
3) Measure voltage drop across resistors. Because the resistors are 1 OHM, mV = mA
Having the full B+ running through your meter is a recipe for disaster. You may not get a second chance.........
EDIT: It may not be clear in the second pic, but the 2 resistors are connected to the center terminal on the terminal strip, which grounds the cathodes to the chassis. Sand the paint off the chassis under the foot of the terminal strip to ensure a good ground connection, or run a ground wire to a preferred location.
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