Re: what would the result be if you added pickups over the strings?
An interesting side effect of the existing pickup-under-string layout is that the waveform it creates is asymmetrical as a result of the string swinging near-to-far, and then far-to-near. If you have a pickup above and below the string, you would have a symmetrical waveform, because when the string swings away from one pickup, it swings towards the other, for every cycle of movement. There's nothing wrong with an asymmetrical waveform, though, so to a degree, it's a solution in search of a problem.
The pickups would have to have a congruous magnetic polarity, so that the same polarity is imposed upon the string, and not causing a cancellation to occur. This would also have the effect of making the magnetism of the string even stronger, improving the output somewhat. One of the two pickups would also have to have it's wires reversed to put them back in phase with each other, so that the currents produced by each would add together, rather than cancel out. This would also serve to increase the output voltage.
Of course, the overall design doesn't make for good ergonomics. Maybe someday really tiny pickup will be invented that could site beside the strings, or above the strings, but closer to the bridge and with a low profile.
