I'm not sold on the fact that Run is not a speed increase. I think that's a shaky interpretation of what's actually written, and difficult to believe that it was what was intended.
I'd say that what is written supports the idea that a Run will not increase your speed, so that a double-move while slowed can only get you 4 squares of movement.
I also disagree with the implication that the Run bonus wouldn't be factored into the double-move twice. The Double Move states that it's the distance of the 2 move actions, and both of the move actions individually have the Run bonus (if they aren't slowed).
If I am right about Run not allowing a bonus of 2, then a double-move while slowed can still only net you 4 movement. However, even if I were wrong about the Run, the Double-Move clearly says you have to take the same "Move Action" twice in a row, and Run is a Move Action. Even under your interpretation, a slowed double-move should be 8, not 6.