The spirit of the challenge is the 'one ride' aspect (though, as an aside, and as someone who never stops at cafes, I've wondered about the ethics of long cafe stops sometimes!). There's certainly nothing in the rules, or good sense, about the ride not going across midnight though, so late afternoon or evening starts are surely entirely acceptable.
Further to that, I can't see anything to suggest that you can't use one ride in two challenges. Obviously, if that breaks your personal sense of 'right' then don't, but these seem to me to be independent challenges. Specifically, why not count a 100+km Lunacy ride in the Metric Century challenge, in that the former is not month dependent in any case, and the latter attributes points to 'excess' rides, so why exclude it just because it constitutes a Lunacy ride?
As I've opined before, these challenges are, ultimately, about providing motivation to ride, so I suggest you do whatever you think will provide you with that motivation, whilst also being both challenging but possible.