So while I have my software firewall off (I didn't make any changes to my router) I uninstalled SiteAssist Professional 1.0.7. Closed both Adobe Extension Manager and Dreamweaver and trashed the file MacFileCache.dat (from my user library) once again.
I reinstalled SiteAssist Professional 1.0.7, launched Dreamweaver and tried the extension again. And for the first time I'm able to enter my activation number for this extension.
I guess I'll continue to toggle my Mac's software firewall on and off as I need to use the WebAssist Extensions. Unless I hear otherwise from WebAssist support. I'd rather not go through this crazy activation ritual any more often than necessary.