first of all you dont edge, you ride the board flat like a raceboard.

you need to sign your kite from left to right, to keep the apparent wind in it. The fins wont help, as you hold and edge not a fin.

Apparent wind theory 101. No.1. if you have a 10 knot head wind and on a bike and travelling directly into if at 5 knots, Whats the apparent wind on your face?

If you have the same conditions and go downwind at 5knots, whats the apparent wind on your back?

Its why sailing boats put up a spinnaker to go downwind to hold their speed, we can sign our kites to do the same thing. I hope this helps

I find it also helps to ride with your most natural stance ..... If you are goofy ride down wind with your right foot forward then carve the board a bit like you would a skateboard...... ie: edge to edge......
You need to keep tension in the lines when going down wind and the carving motion will create the required drag.
As Kit33r said you can only go directly down wind at the wind speed... If you find you are ending up under your kite you can quickly throw in a down loop to pick up kite speed.

Bigger fins will make a difference if you want to ride the board flat as they will help it track in a straight line but if you use the edge style carving they are not necessary.