The QTR adjustments work with print descriptor files rather than .quad files and so Piezography does not really support any of the QTR adjustments - or rather other way around. They were not designed for adjusting Piezography curves. What you can do in Print Tool instead is to use a Piezography ICC to make the prints a bit darker. - especially in the mid to lower end. You would set Print Tool color management to Print Tool Managed and then select the Piezography Matte Print.icc. It will change the printing characteristics from purely linear to more like the contrast on uncalibrated displays.
If you have a calibrated display and your brightness is set quite low in the 80-95 candelas or L range - you could instead use this profile to Soft Proof and adjust the darkness of the print that way instead of in Print Tool Managed…
I think you should try the 1st method and use the ICC in Print Tool Color Management as I mentioned above!
Let us know!
Best,
Jon