I am sorry but it is not clear to me what you are trying to do. If you are using Piezography as instructed on a properly calibrated display - then the output will match the screen. It is very easy to use Piezography incorrectly and the output will be too dark or disturbed.
Because you see some correlation between Piezography curves and Photoshop curves, you give me the impression that you are not using Piezography correctly and may have not read the NEW Piezography Manual.
Let's start here:
What is the name of the curve you used to print the Ilford Fiber Silk. Please type the name as you select it in QTR. That is a beginning. Please send me screen shots of your workflow.... The QTR driver window - any other windows you are using to print. So I can see what it is that you are actually doing....