What I've done in the past and what I'd do again for a 6am ferry is :-
1. Leave the NW about 6pm the night before, you'll miss most of the traffic then and will hit M25 / Dartford at a good time. (crossing is free after 10pm)
2. You'll reach the Services just before Dover (that say 24 hour but weren't) but there is a Shell garage, for between 10:30 and midnight, depending on traffic and how many stops.
3. Recline the seat and sleep in your car for a few hours, set the alarm for 4:30, you can wake up, get a coffee etc from the Services or Shell if services are not open and it's about 10 to 15 min drive to port from there.
4. You'll get there for before 5 leaving just enough spare time, and at least you've had a few hours kip. Sleep a bit more on the ferry and it makes driving much safer the other side then.
You'll just be too fooked going through the night without any sleep and make silly mistakes driving imo.