LOL: saving settings to the project is an _existing_ option in the Debugger plugin.
Knowing what to look for made it easy to retrieve what it does, and it is pretty much what I would have wanted. It does not automatically jump back and forth between the project and non-project mode: that is OK because I plan to use the project mode all the time anyway (for that very reason).
Thank you all for your help, and sorry for taking your time.