I think you would likely experience problems with phantom lights on the 17V line if you used LEDs (ghosting).

I don't use LEDs, but doing some math using Ohm's law should allow you to solder some resistors to the sockets to balance the circuit. You'll have to do some measuring and figuring, but you can probably make it work without burning out too many LEDs.

High power resistors would likely be needed (cement/ceramic).

If I was doing it, I would suggest making it work with a standard 6V LED.

Would 17V be enough to make it function, though? There is no 20V rail. And dissipating the heat from behind the light board would be easier than the heat likely generated from a 24V led that was lit for a long period of time, I'd wager.