There would be no ways to “circumvent” it, if it is really on your previous developer’s own account, as your first post indicate.
In that case, the only alternative would be the procedure mentioned in the linked thread above.
You would gain access to control the domain going forward with the referenced procedures, but all the previous settings would (unfortunately) be lost.
Given a “migration” is planned, it doesn’t sound like losing the previous settings might be a such big deal after all?
If your previous employee/developer, let’s say John Doe, had the email address [email protected] (example.com being your organisation’s domain), you could always try to re-enable [email protected], for example by having that address forward it’s messages to you.
Once you’re certain you’ve re-enabled so you can receive messages sent to any previous addresses/aliases that that John Doe might have had, you would go to this link:
→ https://dash.cloudflare.com/forgot-email
Here you insert your domain (example.com), within a few moments, you should eventually receive a message, assuming that the previous Cloudflare
If you do not receive anything with this procedure, the current account is likely gone forever (due to being the old developer’s own, and not in any way yours).
In that case, you would would have to move on with the procedures mentioned in the thread I linked above, which would be by creating a new account, and though your domain registrar adjust the name servers to match the ones assigned for your domain, in the newly created account.
The mentioned “domain registrar” would be the place you pay the yearly fees for your domain to.
