The discrepancy between the contents of the Quran and the hadith literature was always a bit of a puzzle. Sure, the hadiths are less accurately preserved, but overall the picture they paint is probably pretty accurate. It doesn’t seem possible that women could not have ceased worship during menstruation, for example. That cannot all be fabricated.
I couldn’t come up with an explanation for why Muhammad would add to the words of God, or even apparently override them (e.g. wiping socks instead of washing feet in wudu). The best I could come up with was that the non-Quranic things were pre-existing customs that were allowed to continue.
Another thing that struck me was how different the two are in emphasis: the Quran is more philosophical and the hadiths are more legal.
Having accepted that Muhammad was not a prophet, it has all fallen into place in my mind. The Quran was not central to everything, but was just one part of the authority that Muhammad had. It contained those matters about which external verification was needed: it let other parties know where they stood with the Muslims and with Allah. It didn’t need to contain much law, or ritual, because the followers of Muhammad accepted this direction straight from him. There was no need for it to come from the mouth of God. In a way maybe the Quran was more often for non-believers than for believers. It was poetic and persuasive and tried to win them over.
I also no longer need to believe that Muhammad was always consistent, and so contradictions between the Quran and hadiths – and between hadiths – do not need to be explained away as “inaccuracies in preservation and transmission” (although I’ve no doubt that is one cause of inconsistency too).