Can I restore from a 16GB backup to an 8GB iPhone
Ok, I got it done, but it took a little bit of a run around.

I had failed to mention in my question that the size of the original 16GB backup was indeed close to 16GB.  Clearly not going to fit on the new 8GB phone.

The very first time I tried to restore from backup, I got a message about the size incompatibility.  Every subsequent time it would just hang at "Estimating Time Remaining..."

Next, I decided to remove much of the superfluous data on the old phone, to get a new backup of it under 8 GB.  Trying to use this new, now smaller, backup resulted in the same hang up.

At this point I thought it just might not work.

With nothing to lose, I decided to have iTunes restore the phone to factory.  Then, the very first thing I did was try to restore from the new smaller backup...  Success!!

Somehow the failed attempts before hand, were keeping the phone from successfully restoring from backup.