Earlier quoted context omitted.
Possibly stupid question: Is there any fundamental reason your corporate email system couldn't, for example, just not interoperate with the rest of the Internet, at least by default? I understand if this doesn't work for people in sales or consulting or whatever, but 90-99% of my work email is entirely within the same company, and I think it would be less onerous and more secure to just block external email by defaul…
What we do (and a lot of companies do) is append [EXT] to the subject line of any incoming message from outside the org. Blocking external email by default will drive people to use their personal gmail for work.
A friend of mine works in industrial safety. He sees this a lot. He told me the rule "Jedes Verbot braucht ein Gebot", which roughly translated means "Every thing that is forbidden should be accompanied by a permission". So you can't just forbid people to smoke somewhere, you have to find a place where they can smoke. Otherwise they might find one themselves.