Sorry I don't see your point or rational!
Perhaps I am missing the point because all the loops I have dealt with to date are lightweight or something.
If you increase the derivative influence to the point where a few degrees of movement takes 10 mins you are simply hog tying the whole system.
You may have a ramp but you cant control its duration or rate, well not without effort and complexity.
If you fiddle with it enough you might find settings that get the system to where you want in approximately the time you want
but it isn't going to stay there because it cant adjust quickly enough.
When some external influence causes a positional error it will take a long time to correct the error.
I don't understand why you would want to make things harder, less accurate and less flexible all for the want of a counter.
But that's just me....