Best explanation for 666 I've heard before is Arcanum 6 (struggle between love and pleasure) in the head, the heart, and the sex. The Lucifer is the deceiver, but it takes two to deceive. Beast is just something not HuMan, unattached to the Human Soul/Karma, so it can bring wrath and do what naturally has to be done for the sake of karma.
Remember the mark of 7 Ps on Dante's forehead? I wouldn't think this having anything to do with the 7 sins, actually, but rather more likely to be about the Arcanum 7 (The Chariot/Triumph/Strength) being on the head, the heart, and the sex. People that do alchemy say they receive Arcanum 7 after transmuting their sexual energies. They say that by looking deep within the human organism and the seed you find the philosophy stone/vitriol.
Actually the seven vices can be thought of as being transmutable with the Vitriol/Philosophy Stone.
There are seven musical notes/seven colors of solar prism/seven chakras