I tried this a couple of other places, and they're saying ITC Zapf Chancery, but while that is a fancy-schmancy match, I'm almost positive there's a freeware equivalent that comes packaged with Word that I'm missing. Am I right?

The "other places" are correct, it is Zapf Chancery.

I'm sure there are knock-offs, but none that I know of are included with MS Office products

I was afraid of that. Oh well... time to hit the font web with a stick till I find it free!