I've just had a batch of piezo preamp circuit boards made by makepcb.com, and given them a first round of testing. Here's the results!
Test Setup 
I built up several boards, but I'm only using 2 for the tests. One is built exactly as the circuit diagram. The other swaps out the 500 Ohm resistor for a 150R. This increases the bias current, which should give more gain, at the price of a bit more noise. I'll refer to these as "Standard" and "High Gain". These have standard piezo discs attached to them. I'm also testing with a piezo disc attached to a similar length of balanced cable, and fed into the mic pre via an XLR.
All tests were done using a focusrite saffire 2i2. To start with, I set the gain knobs so that I had reasonable (non-clipping) gain for all the signals I was going to use. I matched the channel gains by using the same disc+lead in both channels, and adjusting the second level to match the first.
All signals were produced in my laptop, using the transmission from the speakers through the desk to the the taped down piezos. This is not ideal - in particular, there's very little LF response. But, it was the best available option.
Test 1: Background Noise Level and Test Tones 
Connected mics to levelled Saffire, looked at ambient noise level: Unamplified: -71dB Standard: -54dB High Gain: -53dB
Conclusion: with little signal present, there is approximately 22dB more noise on the preamped boards. This may is largely electronic noise, although some may be better transmission of low frequencies.
Played a test tone (440hZ) on the laptop. Adjusted gain in software until the level of the unamplified mic was the same as the test mic Standard: +5dB required High Gain: +9dB required
Test 2: Sweeps 
Connected mics, played a sweep from 100Hz to 5kHz. Audio files below.
Conclusion: they're all pretty lumpy. Can see a lot more signal on both the amplified ones. The High Gain seems to have more of the 2k resonance, but that could also have a lot to do with test setup.
Test Sweep Recordings 
Test 3: Tone and Noise Spectra 
Played 220hZ tone, captured spectrogram. Same for white noise
Test 4: Material 
Connected mics, played some guitar, drums and speech, and recorded output.
Test 5: Residual Noise 
Played the guitar part, and recorded some silence after it. Normalised so that the guitar was the same level for each, and recorded residual noise.
Test 6: Shortened leads to piezo 
On a whim, I tried shortening the lead between the piezo and the preamp to approx. 15mm. (In the picture at the top, you can see their original length of about 150mm). Playing a test tone, it now required +22dB to bring the unamped piezo up to level, which is a huge improvement.
Recordings of test tone+noise, normalised 
Short Lead, amped:
- The preamp doesn't seem to be a magic bullet. It helps, but it's not a game changer. It's a bit noisy, and some of the gain improvements are a bit marginal.
- Having short leads between the piezo and the preamp seems to really help. Possibly replacing them with shielded cable could really help.