I thought I was clear that I had already done that (poured water into
the bowl) and it ultimately didn't go down, so I manually emptied it.
But for the sake of thoroughness I did it again last night--with the
same results. It hasn't gone down one iota.

If the water you pour in from a bucket doesn't go down then water from
the tank isn't going to go down. The only difference between the two
methods is that water from the tank will swirl around and help to give
you a cleaner flush.

Have your tried a plunger?

Steve B.