Why such a dramatic drop in power when the handlebars are lower than the seat?
I agree with the biomechanical hypothesis already mentioned by @DanielRHicks.

Every joint/muscle-group has an optimal range of motion and an optimal max-force/max-power position.

I am the same height as you, and the distance you mention is pretty short indeed, as measured on the bikes I ride.

There seems to be necessary to analyze the "cockpit triangle" of your bike: bottom-bracket/saddle/handlebars: in the hypothesis that, lowering your bar, you get an angle between torso and thighs that is too acute, then the correction of the problem would be opening that angle.

That could be made in two ways:


Rise the handlebar (which apparently is the opposite of what you want to do);
Move all your upper body front by putting a longer stem AND moving the saddle forward a bit, so that you feel the pedals "more behind" than in the current position.


As observations:


High power output (a.k.a FAST) bikes, with aggressive riding position, tend to throw the rider over the bars, so that the torso weight can counter-act the torque on the pedals, and also be more aerodynamic. It is common to see such bikes with high, forwarded and sloped seats (extreme example: time trial bikes);
If you just put a longer stem without bringing the saddle forward, you get in a more "superman" position, actually DECREASING the torso-thigh angle that we would want to increase.


Finally, there are mysteries in finding the perfect position on a bike. Perhaps even sub-conscious factors of varied nature might contribute for a sensation of "not-right". Unfortunately, only self-analysis and trial-and-error are the guaranteed key to salvation in this case, although some professional advice would be always welcome (a.k.a. bike-fit).

Hope this helps!