Be careful of some OCR software as they replace the source file with the recognized text. The good thing about Acrobat is that it adds a text layer to the original document. Most new software does that nowadays. So even if something is really off in the text layer (copy+paste), you can see the original document.
I'm not sure if Acrobat Standard has it, but you can batch recognize text in Acrobat Pro. (I don't think it does.) I.e. go back and OCR all of the II. You can even set up a batch sequence that will monitor a folder and will recognize text within the PDF documents arriving inside. Would be good for a fax board or PaperPort incoming faxes. Acrobat's OCR will even auto-straighten the original document. I do wish it were cheaper. You could probably just get one license for the server.
Does UpDox have OCR on their faxes? Do faxes come in a folder?