OK --- this worked --- however, I ran into some glitches along the way which took a while to figure out, my not being an expert in the Score part of Logic.
I figured I'd document what happened for the next person!
First of all, my score consists of multiple tracks, as I mentioned in the initial post. When I dropped the multi-bar rest symbol, I dropped it into the TOP staff. When I then double-clicked on the rest symbol, instead of getting the expected dialog to adjust the length of the rest (per the manual), it just replaced contents of the multi-track score with the single staff....I could not figure out how to get back to the multi-staff score so I had to keep going back to the main track window and regenerating a score view from selected tracks. (There must be a better way!)
Anyhow, I eventually discovered that if I dropped the multi-bar rest symbol into the BOTTOM staff, then double-clicking did indeed bring up the dialog where I could set the length to auto at which point everything worked just as I expected.
Many thanks for pointing me in the right direction.
(P.S. for your original comment, I originally clicked on "Helpful Answer" and then I discovered that I could not change it to "Correct Answer". If you know how I can change it, that would be great)