I put white dimmable leds in mine. They do work with the dimmer but maybe because I only did the ones in the dial cluster? Maybe there's even a mix of leds and the original ones. The white does look different and less authentic but for me it's already a plus that it works.
All LED's are dimmable, but since the current consumption is much lower than an incandecent bulb, the rheostat will normally not really dim the LED's. Do you have a link to the LED's you found?