Arduino MEGA current draw predicament

CrossRoads:
I'd also consider replacing the bulbs with ultrabright LEDs instead. Using 15,000mcd whte LEDs drawing only 20mA each, arranged as strings of 3 or 6 or 9 per digit and driven from 12V with ULN2803 as the buffer, would be quite bright also and use less energy.

This clock is more of a novelty. The incandescents and relays are a key part of the design.
Also, the input waveform for these frosted 130v 60Hz bulbs will be chopped thanks to some household light dimmer(s). This will maintain a comfortable brightness for a kind of warm look.