I’m not quite sure where to begin here, but other than your first step, I think it is all wrong. May I ask how you came up with this procedure? I don’t think it is from the Piezography Manual.
First, the answer to your question is NO! Leave your image file in Gray Gamma 2.2 ALWAYS! There is no need to change the image profile ever.
Soft-proofing is setup and turned on/off in the View menu. It is used to simulate the effect of an ICC profile. It does not simulate the effect of a QTR curve. The terms assign and convert have very specific meanings in this context. I think the term you mean’t to use is select, but I may be wrong. Personally, I don’t use soft-proofing at all.
QTR curves and ICC profiles are two different things. With PiezoDN, you must use a QTR curve. Using an ICC is optional. When using only a QTR curve, No Color Management is selected in Print Tool, and the curve is selected in the QTR setup of the Print dialog. When using an ICC, Application Managed (PrintTool Managed in the new version) is selected in PrintTool, then the ICC selected, and Intent is set to Perceptual. The QTR curve must still be selected in the Print dialog. It is important to understand that the ICCs are derived from a specific QTR curve and must be used with that same curve to get predictable results.
Have you made (or are you making) your own QTR curves and/or ICC profiles for your own particular printing methods? Or are you trying to use the IJM provided curves and profiles? There is a chance that the IJM curves and profiles might work for you, but in the end you will get much better results if you calibrate PiezoDN to your own system. It is a little extra effort at the beginning, but the results are well worth it. I’ve been doing this a really long time (Pt/Pd and other alt-processes) and the chance that any 2 printing systems are the same is minute - there are just too many personal variables.
Assuming you are using the IJM curves and profiles, have you printed one of the target files to check whether they are linear with your printing system? That would be a good place to start if you haven’t done it.