Relays/Shift Registers/Arduino Interference from TL ballast

ORiON:
The relay boards are optoisolatd using it's own power supply.

I think I see that you have connected relay board ground to 74HC595 and Arduino ground.
That makes them NOT opto isolated.

Relay supply connects to JD-VCC (jumper removed) and relay ground.
74HC595 connects to relay VCC and relay inputs. NOT to relay ground.

This might have nothing to do with the problem you're having.
Leo..