You actually can de-link them, though it's a bit of a pain and involves making a new email. It's a little hard to provide visual instructions from a phone, but I shall try:
- Add a new email to your Workplace and Productivity accounts
- Set those emails as the default account for both of those sites
- Remove your old email from those two accounts
Voila. Two logins, two emails. Note that it might take a day or so for reputation and flair to update on the main StackExchange website.