I was able to finally figure out how to do this. Here is the process we used in case anyone else wants to do the same.
1, Go to the course in question, and "export" the gradebook with names of enrolled users and the activities
where you want to enter grades (in our case, this was the final exam empty fields).
2. Open up the exported file in Excel and bulk enter a passing grade for all the users in the final exam (we used 100%); save as a CSV file.
3. Import the gradebook file back into Moodle, making sure you map the fields correctly.
4. Temporarily delete ALL of the restrictions on the Certificate; new certificates should then be automatically generated for each user with the new data (you may have to purge cache); if you have checked the option to e-mail certificates, they will be immediately sent out.
5. Re-enter the restrictions back on the Certificate so that all new users on Moodle will now have to meet the requirements to get their certificate.
6. The users who had previously completed the course, will still see the restrictions if they try and access the course again.
7. However, the new certificates generated are available to users in their Profiles, and/or e-mail (if this was set up), and the teachers / managers have a record in Moodle as well.
This may not be the most elegant way of doing this. But it did enable us to do what our client needed.