I know that mine, like Tim's was wirewound, and I can remember hassling
with a replacement. The wire was very fine and susceptible to
breaking.

These days, if I wasn't too concerned with keeping it exactly as EICO
designed it, I'd probably use a power mosfet with a small heatsink, as
a source-follower driven by a lower-power higher-resistance pot. I'd
include a zener from gate to source, and maybe a 10 meg resistor from
gate to source (in case the pot wiper opened) and maybe a 1 meg
resistor from pot wiper to gate (to limit max pot wiper current). That
would provide a fairly "hard" voltage output at the FET source, which
could be "softened" by adding a resistor in series. It may be useful
to drop something like 220k ohms/1W to ground from the output, if there
isn't already a resistive load to ground in the circuit. The parts
would likely be easier to find than an appropriate direct-replacement
pot, though maybe not.

Cheers,
Tom