I have stuff that will present a high impedance to the pickups - but had sort of guessed that the existing preamp probably did that, or was so intended. I imagine it's worth a try hooking them up to a different preamp.

There is no way that the existing little pickup things could ever have been under pressure from the existing removable tune-o-matic saddle assembly - but I agree pressure on piezos results in higher output: the same pickup is shedloads louder in a 12-string or a mandolin - about 20db up in comparison with a 6 string I'd guess.