Newark local here. At that time of night there is very little traffic on the A46. The roundabout is big but only has a couple of exits so it looks worse than it is, and the whole section is street lit. The Winthorpe route has a couple of bits where you have to dismount because of the anti-motorbike railings (under the A1 bridge) and that area can collect quite a lot of broken glass on the cycle routes (especially under the A46).
During the day I'd definitely use the cycle route as the traffic is pretty bad, but at that time that stretch of the A46 is a reasonable option.
McDonalds is 24 hours and there is also a 24 hour garage on the A46 just before the roundabouts.