Is reiki therapy a good way to reduce my dependence on pain pills?

Yes: Yes. I am not a fan of cam, but I am not a fan of opioid dependence either, so any modality which is reasonable and "helps" pain is a worthwhile trial.

No: Reiki is nonsense. Its mostly helpful in thinning the wallet. It would be much better to see a physician experienced in pain management and medication detox. That stated, there are many scientifically valid non-pharmacologic behavioral strategies. A pain psychologist can help here.