Thanks for the tip with the downshifting, but those brakes are going to heat up no matter what since I will need to apply them anyway to get down hills that have steep curves. Downshifting doesn't hurt anything?

I just had the front end checked and had 2 ball joints replaced and they didn't say the tie rods were bad. I grease them every oil change anyway, so I hope not. I didn't notice any play in them last time I had the wheel off the ground. CV axles were just replaced a couple years ago. Since it stops when I hit the brake, it would seem that that rules out everything but brake-related parts. But I may have found a lead in the "investigation". I looked at the hole in the backing plate and found something interesting. Not only was there a hole, but there were jagged edges on the edges of the remaining metal and there is what looks like a deep scratch on the inside of the braking surface of the brake rotor where the backing plate is closest to the rotor. I think I may have found the probable cause of the noise and the possible scenario. When the brakes heat up in the mountains, that backing plate expands just enough at the closest point to the rotor and hits it. Since the rotor is possibly warped, it will do the click-click-click-click- scratching sound. But since I hit the brake, it will hold the rotor straight and pull it away from the plate. The question now is the cure. Do I have the shop cut off the part of the packing plate below the parking brake mechanism on both sides? What about the rotor? Do I leave the scratches on there or have it resurfaced? Thanks.