I fired mine up again and took some readings. With the cap on the secondary the meter shows 13.7 V. Without the cap it's 19.8 V. This is with the meter in parallel with the cell's wires. Then I removed the cell's connection to the non diode side of the AC input (the wire which doesn't go directly to the transformer), and put the meter in series at this point, in series with the AC wire and the cell. With the cap, it shows 2.8 Amps feeding the NST, through the meter and the cell. Roughly 38 Watts. Without the cap it reads 3.9 Amps, or right at twice the Watts.
I took a video, to get a clip of the bubbles right at startup, before the water gets too cloudy, but Windows 10 won't play the video from my Android phone.