The "weird little box" is a wirewound resistor. It is part of the power supply for the channel switching.
Schematic calls for a 680ohm 1w in that spot but when that blew up whomever did the fix probably threw in what they had. If the channel switching works ok I wouldn't be too concerned...
What you are doing and what is being suggested to you is like eight different kinds of wrong.
Return the value of the resistor on the input grids of the output tubes to their original value (1.5k or whatever was there.) Do not install a trimpot in their position.
Leave the 220k bias feed...
