Personally, it seems more likely to me that he never expected to get away with it for as long as he did, didn't really have a plan beyond getting out of NYC, and went to that McDonald's to get caught.

Maybe I'm wrong, that's completely possible. But... I dunno... a lot of eyes are on this case. It would be very very dumb of the cops to manufacture a suspect with all the attention on this. Maybe they are that dumb...