Arg. If you still have the "good" probe, I've found how to get them move: the motors pins were identified (see bottom of this document ). I haven't documented it, but using the same picture, you can put 5V on pin3 and GND on pin17, and you'll get a 1.4V peak on pin2. That would enable you to determine the absolute position of the head. The motor can be powered at 5V using pins 8 and 9 (the neighbours on the right of pins 2 and 3).
That being said, I've been able to do calibration tests using a backing-less piezo bought at 2€ on aliexpress - those are ~2MHz piezo but have the same behavior as usual piezos (with a longer ring time). You can see their behavior, I was testing my ADC board on them on this doc, in the Testing with a piezo with no backing section (or image attached) =) You'll see the ringing time is 40/50us - but still you get a signal to play with.
A team (on the slack i guess) wants to use dual element transducers to do A-mode imaging - and they have found dual elements such as that -- again aliexpress =) )
I still have a testing piezo I had bought at 200€ 2cm dia, 1cm deep, bought from smartmaterials - if you want I could resell it to you (or exchange for mems / cmuts - it's what i'm after). The advantage of this one is that though the form factor is not miniaturized, it's a quality you'd expect from more serious suppliers at half price. For transparency at the time, I had tried a benchmark of piezo suppliers but I couldn't find a better mix of quality vs price.
Anyhow, let me know if you do some more research on suppliers, I'd really be curious to know where to get some good (other than ebay) at a good price straight from the suppliers..