Ostensibly, I would like to use the format "h:mm", which does not
display AM or PM. But I want it to always display 12-hour time,
ignoring AM and PM, not 24-hour time.

Is there a format (standard or custom) that will do that
automagically, without my resorting to a formula?

(I am using Excel 2003.)

If I enter 10:00 in one cell and drag down, the time after 12:00 is
13:00. I want 1:00, just as I would get if I used the format "h:mm AM/
PM". (But of course, that includes the AM or PM suffix, which I do
not want.)

To get what I want, I have to manually change 13:00 to 1:00, then
start dragging down again.

That's a drag :-).