(The following is unproven. After a few experiments, I will either remove this line or delete this answer.)
My question was off in one important detail. Turning the handlebars up simultaneously makes my back and my wrists happy. The issue then is not whether to turn it up, but by how much.
A bike fitter is no doubt helpful, but a personal cycling instructor, one who inspects a cyclist and points out what they're doing wrong, may also be helpful, and in a complementary way. In a sense the former fixes the bike; the latter fixes the cyclist. The discussions here acted as the latter.
The solution (and this is personal, i.e. YMMV) was to learn how to use the hooks position properly. I cycle on asphalt trails, shared with adults, unpredictable children, and wild ducks and geese that think, correctly, that they own the place. I was hence putting fingers 2, 3, and 4 (counting with the thumb as finger #1) on the levers, all the time that I'm on the hooks, which is most of the time. I'm not sure why I did that. I don't drive with one foot perpetually on the brake pedal, but on a bike I figured I might as well be perpetually in the "ready to shift or brake" position. Having recently moved from an MTB may have been a factor. On an MTB it's not really feasible to keep the thumb and index constantly on the rapid-fire shifters, and a new road cyclist may be tempted to think "here is finally a shifter that I can hold all the time."
It may be more sensible to hold the handlebar, and to move fingers 2, 3, and 4 to the levers anticipating the need to shift or brake, then return to wrapping the fingers around the handlebars.
Moral of the story: if your car has a manual gearbox and you sometimes keep your right (left in the UK etc) hand perpetually on the gear stick (gearshift/shifter) since 1- you're shifting frequently in traffic, 2- you have no other as useful position for that hand, or 3- that's more comfortable than constantly dragging that hand between the 2 o'clock (10 o'clock..) position on the steering wheel and the shifter, you may have decided when starting to road cycle that putting the fingers perpetually on the levers is a good idea. It isn't. Holding the levers turns the wrists up by an angle that makes the carpal tunnel no longer straight. That is ok while shifting, but it's not a good position to keep for long.
If the above holds, it's unclear what useful customization is provided by an adjustable stem. Possibly, an adjustable stem fine-tunes the size of the bike frame, making an off-the-shelf bike size better match the rider, who would otherwise be somewhere between two sizes.