Is this in-circuit with the antique capacitor C4 200uF 6V across the meter? I'd expect that cap to be defective, along with every other electrolytic given their age.
It would be strange to have such a high full-scale current, you seem to be around 3mA. The 6AT6 is rated 1mA max. plate current, so the meter movement seems off.
There are some mods to limit pegging the panel meter hard, hopefully it is not damaged. Try a much smaller series resistor say 1k with your power supply and closely watch the meter movement, for sticking, or linearity if 1/2 scale is 1/2 the full-scale current if you can get there. You can measure the panel meter ohms as well.
I have seen contamination inside (metal chips) cause problems as well. Had to do surgery and use masking tape to pick up everything stuck to the magnet inside, of panel meters.
Check closely the meter faceplate for any text about the meter movement. It might match other B&K tube testers but just have a different faceplate.