I followed your instructions, turning my iPhone off, then back on. And placed it horizontally in the stand. At first, it did not charge. I tried turning my iPhone to vertical, just to try. Still nothing. I then took off my waterproof case, and went thru the same procedure. The case is not what I would consider heavy-duty, and the plastic back is really not very thick. Nevertheless, to do a fair test, I took it off. Went thru the same procedure again, turning my iPhone off and back on again, then placing in the stand. Low and behold, it began charging, but only when lying on one of the sides, the side with the power button, I believe. I then decided to push the limits a bit. Very carefully, I rotated the phone 90 degrees to vertical, taking care not to lift the phone away from the stand; keeping in contact with the plate, in other words. Again, unexpectedly, the phone continued to charge, in the vertical position.
I will not necessarily call this a complete win, however. I fully intend to keep my phone protected and in a case, waterproof most likely. The case I have, I got from Amazon for roughly $23. I could have sworn that someplace, either on the Amazon site, or on the packaging I received the case in, it said that the case would not interfere with wireless charging. However, I did buy 2 cases and it may have been the other case that I read that on. I'll have to test the other case now, as I took my phone out of it, preferring this case over it.
I'm still hoping for a fix to this problem eventually from Apple, so that I can use the stand AND my case. It obviously sounds like this is some sort of a software problem to me, which I hope they can fix.