I think it is more complicated. The protein in the APF provides structure to hold the dough together. The oatmeal would not replace the protein lost by reducing the amount of flour.
Once you change the recipe that you love it is no longer the recipe that you love; it is completely different. So, if you start with the premis that you are now working with a completely different recipe, I would suggest looking at oatmeal cookie recipes to see what, if anything, looks like yours and start tweaking from there. Or just find a good oatmeal cookie recipe and stick with it.
I should talk. I've never made a successfull cookie in my life!!!