Ken, Ken, Ken - you must have missed the fine print in my experiments,or it could be my foreign Australian accent. Anyhow, dulcimer tops are between 1 1/2 and 4 times LOUDER than the backs (measured directly above or below).
In the one instrument where I added a false back there was very little change in the front/back loudness on the lower fretboard compared with the same instrument without a false back - the top was 1 1/2 times as loud as the back with or without a false back. But above the 8th fret the the addition of the false back increased the relative loudness of the top to three times as loud as the back. So the addition of a false back increased the top loudness in the high frequencies somewhat. These are actual and accurate measurements of sound pressure level.
But listeners are more likely to be to one SIDE of a dulcimer rather than underneath it, and my impression was that the false-backed arrangement did seem louder from the side than a similar shaped and configured instrument without a false back. My unsubstantiated suggestion is that more of the vibration of the inner back, undamped by resting on the knee, is directed out of the edge vents or holes to the listener, rather than substantially downward as in a single-backed dulcimer. I don't think it produces MORE sound, just directs it where it can be better heard.
I've only made one false backed dulcimer, so can't claim much expertise in results, but I did notice that the outer back (which was thin) still vibrated a lot, and hence lost sound downwards and into the knee. To me it makes sense to try to minimise this vibration of the outer back, and I'd do that by making it heavy and stiff. I'd be interested to hear what experienced makers think of that idea.