Actually... that's kind of the whole point of a sundial? It's a solar time instrument, so if the sun isn't out, it obviously can't work. They were never meant for telling time on cloudy days or at night, that's why mechanical clocks were such a revolution. The real precision issue is accounting for your exact longitude and the equation of time, not just the base alignment. It sounds like you built a correct sundial, it just can't defy its own nature.

My roommate used my roasted veggies in a smoothie, never again!