Putting a capacitor at the 6BN8 grid will filter hum and noise there for leakage-test mode.
But that part's leakage current alone will upset tests and it will kill the bridge mode for measuring capacitance because that uses AC. So I don't think it's a fix.
I would not scope the 6BN8 grid, but instead the plate if looking for hum or oscillating.
If it's a problem, the 6E5 you can pull and see if it's C4 or C11 are making it worse.
You are sure the new filter caps C1, C2 are working, at least 20uF 700V?
I would check the grounding, from the line cord to chassis and R41/R42 and the ground on the 200V side. It also goes to the bridge transformer. It's a few minutes for continuity tests.
The paper, mica leakage test, I still can't find the current-sense resistor. Thought it would be at pin 8 on the rotary switch.
Beyond this, need some pictures inside.