PWM is definitely too complicated for this application.

LEDs can dim - a little. If you want to retain the dimming though, keep the incandescant setup (I meant to make that statement in my earlier comment but forgot). If you try to dim LEDs (especially in an array like ETL is using) you'll end up frying it or the circuit. LEDs try to be constant power so the current will increase dramatically as the voltage drops ... and the LEDs are NOT protected by the fuse.

The more pertinent question is: can ETL debounce his relay so that it doesn't buzz?