I'd like to do military presses primarily for deltoid building, since
the bench press already hits the triceps hard. I find that I can do
partial ROM (bar from shoulder level to top-of-head level) without
my shoulders popping, but if I go all the way to top (lockout), my
shoulders pop as I come down. (No injuries that I remember.)
(These are not many little noise-only pops like my knees do
during squats, but something moving a little--though no pain.)

Is a partial ROM military press like I describe useful for building the
deltoids, or am I wasting my time? I also found that inclined press
(i.e., sitting not fully straight up) allows me to do full ROM.

They will work some.

Try using DB's and using a neutral grip.

The bottom of the ROM is where the triceps are the least help and the shoulders do the most work.

If you can go behind the neck as well in that bottom ROM without problem (though that seems unlikely), you can do Bradford presses.

While I agree with what Chic says on the ROM aspect, I also do exactly what you describe every Friday.

I do mine on a Smith and seated. It is a partial press of about 2 inches at top of movement. Safety catches locked just below bar.

You can absolutely get some horrendous weight in the air doing this. (last Friday I did 275lbs. which in my mind is somewhat horrendous).

It is more of a strength move than a bodybuilder move.

But....although the Triceps are involved I tend to feel it in the Delts the next day. I'm going very wide on the grip.

I had to customize the angle with an extra adjustment hole on the bench to get the exact angle to lift from.(Chairback almost vertical and if you dropped the bar it would almost touch your nose on the way down)

Yours arms don't go to lockout!! Keep it just under lockout.You go up to weight that you can hold up for 5 seconds. (I pyramid up from 150 just for the hell of it).

While this is a strength move you need full ROM ex's to get shape and definition.

One of my favorites for that is the Cable Delt Raise.

If you were doing a right arm raise you would pull the cable from the left and across in front of you. This puts full tension on the entire move whereas a dumbell does not. (sets 0f 12 to 15 reps)

Also Cheat Lateral Raises with Dumbells. Sets of 5 reps to 8 reps.

To nail all the Delt heads you should also do Forward raises and Rear delt work.

Try adjusting a bench to about 35 degrees, lie chest down on it and do Rear Delt raises and Cheat raises.

Also lie on a flat bench on your side. If your left side is down let your right arm hang down to the floor in front of you with dumbell inhand.

Now raise dumbell up to vertical and lower and repeat and then switch sides. Have just a slight crook in your elbow as you raise and lower DB.

Along with the standing DB Forward Raise you might want to try this:-

Adjust a bench incline to 35 or 40 degrees. Now lay back with dumbells in each hand hanging straight down. Raise to vertical and then lower.

This puts more of a stretch on the muscle than a Standing raise. So you use a little bit lighter weight than a Standing raise. However do them both for full effect.