For my sins I used to cycle between London and Canterbury along the A2 quite a bit one summer (early 1990s).
The route at the end of the summer was nicer.
By the end I was doing Shooters Hill (A207), then via Dartford/Gravesend (A226) until onto the A2 where there is an M2 to take the traffic - it's OK that bit).
Then at the end when the traffic comes back I'd take the next L after the roundabout via Blean and Dunkirk to avoid a bit more, then into Canterbury through Harbledown, as you do.
After Barfrestone (famous church), from your route, go vi Lower Eyethorne and strought through Eyethorne towards A256 but take a right and cross over it, where it says Friends Wood. Then West Langdon and East Langdon to Guston (over the Jubilee Way) and past the castle, then at the bottom go towards the sea and turn left for the docks.