Problem replacing screen taps with pots

[old_tv_nut]

Your posted schematic is missing a lot of info on where some of the resistors are connected (what voltage is at each point in the circuit). There is only one way to make sure the circuit operates the same without knowing all these things and that is to replace R243 and R239 with the same total resistance.

I repeat, you will surely avoid trouble and get the result you want (a continuously variable tap instead of only H, M, and L) if you remove R243 and R 239 and replace them with a total of 4k. The way to do this is to wire one end of the 5 k pot to H and the other end to L, and also put a 20k (18k or 22k is close enough) from H to L in parallel with the 5k pot. Connect R253 to the wiper (center terminal) of your 5k pot.

Simple, and guaranteed to work without further calculation.