I wasn't suggesting using reincarnate to price the ring, I was offering it as a standard of comparison to prove that this thing really doesn't need to have a crazy high price. The pricing tables in the DMG are only guidelines anyway, not hard and fast rules by any means and I have no problem with the price presented in the first post.

The reason I don't think it should be an artifact is because that takes it out of the player's hands and puts it into the DM's. If a player's concept involves immortality they should have ways of accomplishing that without resorting to DM fiat.