This sounds like another application thats ideal for the hobbyist with a microcontroller- you know what you want and nobody sells it.
I haven't encountered anything that's close enough to bend to your needs, so you'll probably have to start hammering your own code.
I have given some thought to a clock or calender that would include lunar phase, but no variable illumination.
That being said, don't be surprised if 90% of your program is in the human interface. As for the chip, go with what's familiar or handy. You won't need very many pins, more for setting it than everything else combined (1 pin for PWM output, 2 or 3 pins for the RTC if applicable, 3+ pins for buttons and 2-11 pins for the LCD if applicable, the buttons and LCD could be done away with if you will use a computer to set the clock in which case only two pins there as well).
The functions won't be arduous, so a midrange device will have plenty of muscle. Onboard PWM hardware will simplify your coding substantially. IIC or SPI will help slightly assuming you will be using an external real time clock. A USART will be necessary if a computer is involved.