S mode is basically the settings for engine braking. In my experience, S-1 and S-2 are sufficient to keep the car below 25 mph on pretty steep gravel and dirt. That's the only place I've used it consistently since I didn't want to rely on brakes to moderate speed on a loose surface.
I think that if you used S mode to moderate engine braking, you should be able to just use the brakes as normal. S mode should take enough of the braking load off and moderate your speed so it shouldn't be an issue.
Also, if it helps, I haven't had this issue on any drives I have done, and I routinely drive the Los Angeles crest highway (which takes you from ~1,500 up to 5,000) and up and down from the colorado plateau in AZ (which is fast driving with elevation varying from 1,500 to 7,800).
Your issue sounds like a function of the steep grade and the low speed combining to cause high-energy braking with limited air cooling.
Anyway... try S mode.