I don't see what the problem with the A2/M2 is apart from the odd slowdown to 30/40mph in the 50mph areas, probably due to panic braking from speed cams unless an accident takes place where it'll take 2-3 hours to clear up
FYI, there are roadworks on the A20 at the moment (Lee High Road, just after Lewisham Centre) with temporary traffic lights deployed so avoid it completely unless you know the backroads (as described below):
[Lewisham Backroad]
-When you get to the Lewisham roundabout, you have two choices, the first being the best route, the second being more comfy but with annoying traffic lights slowing down your journey:
1) Take the first left to Lewisham Road and then the first right to Granville Grove, take the first left to Cressingham Road and then right onto Lockmead Road (don't speed between these two roads as there is a huge police presence and also is an accident hotspot as you can't see round the corner). Take the left on the end of Lockmead Road to join up with Belmont Hill.
2) Carry on straight through Lewisham roundabout, when you get to the the set of lights where the bus lane is on the right, take the left to Belmont Hill.
-Go to the end of Belmont Hill/Lee Terrace until you reach the roundabout at the end, you will have to decide whether you want to take the first exit (left) through Blackheath Village and follow route to take you to A2, or take the second exit (right) down Lee Road then left at the junction to merge back with Eltham Road to take you back onto the A20.
-If you decide to take the A2, follow the Royal Parade (stay on the right). DO NOT follow any sat nav. routes that tell you to take the Prince of Wales Road as it is a "no right-turn" at the lights, which means you can't get to the A2. You will need to take the Prince Charles Road at a mini-roundabout (first exit on left) and take the third exit (right) to get on Shooters Hill Road, which then leads you to the A2/M2 route... however, if you decided on this route, you should have just gone straight from New Cross, which would be faster

[/Lewisham Backroad]
The A20/M20 route is probably the fastest route provided there isn't too much traffic (traffic should clear up after Sidcup).
I'd personally use the A2/M2 route, it is shorter and if traffic levels are reasonable, it will also be the fastest route. An alternative route would be taking the A2 only instead of joining the M2, which takes you straight to Sittingbourne. Pray there isn't much traffic at Rochester though as you could be stuck for quite a long time. And any accident on London Road will render that route unuseable.