I'm not trying to rain on your idea, but a thrust reverser will really only work on a turbine not DF.

DF and turbines opperate differently in obvious ways and some not so obvious ways. With a DF you escentally have a prop turning in a housing. It pulls itself on the air deflection from the blades spinning. It does not move forward from the thrust of the air comming out of the tail. This air is strickly a byproduct of its function. Turbines, on the other hand, do not move forward from a spinning fan. The fan is strickly for compressing inlet air into the turbine. It move forward because of the expansion of gas in the chamber is forcing it forward. To recap, DF has an equal amount of air going in the inlet as it has coming out. The turbine has only a fraction of air going in as it has going out (20 to 1). This makes the difference when using a reverser.

At best, the reverser will only kill the efficieny of the DF and make it not go forward any faster, but it will never make it go in reverse. Obviously the reversing force is what slows the aircraft down.

I'm sure it will look cool, but I wouldn't expect it to slow the aircraft.