After some more experimentation, I hit upon a mixed blessing.
Bottom line: I'll use the method below if I have to, but would appreciate anything that would work better.

The following method does work, but trades one set of problems for another.
The good: No worries about image being smaller or not centered.
The bad: it's very hard to get the image located at the right spot. (The Shape method was very easy to move and nudge.) And the results can vary widely even with the same settings. Very temperamental.
Anyway, here's what I did:
1. Insert image (PNG) with transparent background into Word.
2. Recolor: set Transparent color
3. Text wrapping: Tight
4. Set distance from image to zero.
Result: perfect wrap, but not where I set the insert point! The image moved after I set up the parameters.
Tried to include the image result but was too large for the post. I'll try again.