David, I can't imagine doing anything inside Word is easier. 
Courtesy of Mike Wickham, these are the characters to use INSIDE search/replace boxes:
You can use these hex values inside the find dialogue. They can be found in the "FrameMaker Character Sets" PDF, which came with your software or can be found online.
\x22 = straight quote
\x27 = straight apostrophe
\xd4 = curly left single quote
\xd5 = curly right single quote (apostrophe)
\xd2 = curly left double quote
\xd3 = curly right double quote
Typing in the document itself, Esc+" produces a straight double quote and Ctrl+' produces a straight single quote (apostrophe).
Courtesy of David Artman:
Curved apostrophe Find: ALT+0146 (’)
Curved quotes Find: ALT+0147 (“) or ALT+0148 (”)
After this issue, I googled for FrameMaker Character Sets and downloaded it. That would be my future recommendation for everyone.
Thank you all for your help!