It is not so much a characteristic of the piezo pickup but the input stage of the (pre-)amp and the clipping indicator circuit.@SamuelHarris With the original jack I was basically always clipping whatever input I was using. On Felix turned ALL the way down, it still hit red, though it didn't sound like "clipping" - on the AI amp I tried it sounded like a buzzsaw
The new jack appears to have a capacitor in the housing, and allows me to get plenty of headroom. Not only is it not clipping anymore, but as a number of people have noted, with double bass pickups there can be a sweeter, more acoustic sound with a gain setting a fair bit lower than "barely not clipping".
The clipping might be shown when the RMS clips but peaks can clip much earlier than the clipping indicators shows or gets visible clear enough.
The (pre-)amp can clip if the gain control is after the first amplification stage (i.e. FET or valve). Then the first input stage can clip with a large input voltage and the gain only puts the volume of the already clipped signal down. In that case a attenuated input signal helps.
Since piezo signals deliver a very limited current (that‘s why we need the FET/valve preamps), it is better to use a capacitor-based voltage divider (piezo is one capacitor, the other one in the jack in series with the piezo) than a resistive voltage divider (which reduces the input impedance).
Usually foil capacitors are used for a good sound, the value depends on the pickup, but are probably in the nF range. Just in case one wants to make an adapter (cable) with a capacitor from hot input to hot output to experiment with.