OK, let's ponder the ducting idea. I was thinking this over this morning.
First question is does the battery stay on for three days? It would be worth checking out...does anyone have an old flip phone they could run down? Keep in mind that the phone would be searching for a tower the whole time which would tend to run the battery down. Another point to consider: apparently Bill switched his phone off to get into the park. So at some point for this to work he would also have had to switch the phone
on. Which means he would have had to have been somewhere where he thought he could get a call out, and have a reason to call. Which I think rules out a sudden death scenario. I doubt that he'd fall on the phone and it would then turn on. So I think we can still safely assume that at some point Thursday night, unless he falls unconscious for an extended length of time, Bill turns the phone on to try to call for help/give reassurance, depending on what the situation is.
OK, next point, let's consider the location. Here's the map from my website (again borrowed from Tom's) with the places that I'm aware of that you can get reception along the line:

(Referencing to prior posts, the "magic bullet" spot is at 1, and the "UC ping spot" is at 3)
So right away you see the problem; the 10.6 line runs right through Smith Water, and inside the 10.6 line you're on the north side. Further down the line towards the west you have the low-ish (it's not THAT low) hill that both Myth and I checked out, and then you're into UC. I have probably walked about 60-70% of that line myself. I'm not saying I couldn't have missed Bill, but I'm hard pressed to think of WHERE this ducting event might have occurred. You're awful close to roads and trails anywhere in there, in Smith Water you're looking at the north face, and we've already discussed UC. How about to the northeast, up by Park Road? The problem I have with that scenario is that IIRC that area was the route in for many of the search parties (not to mention many of the ones since). I guess if I was told that this scenario was the right one, I'd probably look proximate to where the number "4" is....but....that's probably the most reliable cell reception in the whole area. I've called people from there and had sustained conversations. So I don't know why Bill doesn't just phone home if that's where he's at.
Up by Park Road, I'll tell you what, you can't get a call out anywhere near there, as I know to my chagrin because I got a flat on one of my trips when I was parked there and we had to drive several miles on the rim to contact AAA. Under the ducting theory I suppose that wouldn't matter, but I'm just sayin'.
Thoughts?