Biasing and then feeding into a GPIO analog in, has the risk of undersampling the piezo signal, as it will be sampled at only 3kHz.
After a rectifier, a (simple) analog low pass filter can be used to limit the bandwidth and avoid undersampling.
A half-wave rectification may miss the energy coming from the negative excursion, resulting in a uneven response, so I think a full wave rectifier would be better.
I'd avoid potentiometers for sensitivity control at the input, it is better to adjust this in the patch if the dynamic range allows.
Independent from direct, half- or full-wave rectified input, some patchwork is needed to extract velocity in a robust way, I don't know what feature is the most robust.
Anyway, just some thoughts here, not a tested solution. It is fairly simple to make working triggers, it takes a bit more research to get consistent velocity response. For in-depth research, recording the response at different velocities and inspecting the time-domain and spectral response would be a good start. Probably someone has already done this, I did not find a good article on the internet but only searched briefly.