Have you checked the firing pin protrusion on your gun to make sure it is in spec?
Have you tried comparing a fired case to a FLR'd case? (A case gauge makes that easy)
To answer your question, yes, you can just turn out the FLR die bit to float it. But the more consistent way to do it is to use custom shims/shellholders to give a positive stop at the top of the stroke. When the die is floating, your cases won't get sized to as tight a range. Press flex comes into play, which means the length of your cases will start to vary a tiny bit depending on how hard the brass is and how well you lube it. Also, any increase in wear or slop in the press over time will make your cases grow.
As a rule out step, you don't even need to mess with your die settings. Just use your fired cases. Deprime them with a nail. Take some fired primers, remove the anvil, and hammer out the indent with a nail. Prime some fired cases and some FLR'd cases with these empty primer cups, and see if there's any difference in the indent when you "fire" them. But if your unfired ammo/cases are extracting, the extractor should be holding the case strongly enough for them to fire, even if your headspace is off. Hence, why you're not receiving the answer to the question you are asking. Even if changing your die setting were to solve/mask this problem, it would mean you also have another problem or two.
