1. Four months is very long, plenty of ways to make it faster, you are absolutely right.
2. Adding bacteria is indeed the way to make it faster, definitely should not take four weeks if you dose bacteria. Though recently some products are reported to not work very well compared to others. What brand did you use?
3. No lights is a myth. Lights won't really affect the cycle. May grow algae, but that's a different story entirely.
4. Your 'dry live rock' looks like 'Life Rock', an actual brand of rock from CaribSea. It is dry rock, but coated with microbes and painted purple, or something of the sorts. But yeah, treat it as dry rock, because as far as people could tell so far, it behaves like dry rock.