Parasitic oscillation? Have a scope with low capacitance probe to get some idea of the frequency? Interesting that lifting the shield on the cable "stopped" the oscillation. I would expect the oscillation would get worse with no heavy shield ground, especially to the mic body. There may be a ground loop or an inductive loop (even a loop of wire) associated with grounding. Cold solder joint can cause trouble. Doesn't take much of a wire loop with a nearby high impedance capacitive circuit to resonate and oscillate at some RF frequency. You will probably need to open the mic and go in with a scope since the output transformer won't pass RF frequencies. By lifting the cable shield, you may have shifted the oscillation higher in frequency, upset the operating point of the tube, so the apparent result is decreased audio gain, and the real problem is still unsolved. If you are using a 5840, continuous twist the cathode and suppressor (g3) leads together to their termination, and likewise for the screen (g2) and anode. No excessive lead length. If you really want to do it right, follow the instructions for installing a AC701, including 5 close spaced turns of tube lead (directly out of the tube, for each lead) over a 1 mm drill bit (1/16" works) to provide for heat sink when soldering tube leads so the glass won't crack. Use a good pair of needle nose pliers and no stress where the leads enter the tube. The tube must be oriented so the control grid (g1) is closest to input from the capsule. I assume the tube orientation is incorporated in the kit circuit board... BE CAREFUL working inside the mic, connect test gear with power OFF, then test with power on; use clip-on probes to avoid accidental shorting, make sure mic power supply is discharged before making changes, set the scope input to AC to isolate the DC from the mic circuits. Do not clip the control grid (g1) high impedance connection with the scope or multi-meter. Voltages (and scope indications) at the cathode, anode, or the variable polarizing voltage should indicate what is going on. You may find oscillation in the MHz range. Low gain anode followers usually work, but will oscillate if conditions are right.