HiI think pre-2011 models had an actual signal flasher that could be swapped out with an electronic flasher to solve the LED issue, if I'm remembering the year correctly.
I just stumbled upon this forum. I have almost the exact same issue with my 2011 3.7L Mustang. I replaced the indicator lights with LEDs and now I cannot switch off the hyperflashing. I have the same values in the GEM/SJB Module as you do so I was wondering if you got to solve this issue? First I also thought the car had a signal flasher that just needed to be replaced with one that was "LED proof" but then I could not find a flasher anywhere and somebody told me I had to fix it with Forscan.