Trying to keep track of external courses from inside Moodle is not an easy task, and there are likely to be any number of successful approaches to resolving this. Right off the top of my head, with little or no thought at all, and using the information given, (so not really knowing your exact circumstances) I think I would try something like this:
1. Set up each group of external courses that link together in a single Moodle Course - 1 external course per section. Say Moodle Course 1 is Month 1-3 Section 1 course A, Section 2 Course B, Section 3 Course C. Moodle Course 2 is Month 4-6 and so on.
2. Create an Assignment for each Section which requires Users to upload their Certificate of Completion.
3. Hold a short quiz, say no more than 5 questions, about the course they have just completed in each section.
4. Using Completion Tracking and Restricted Activities, hide Section 2 until the Course A Certificate is uploaded AND the quiz has a result of 100%. Then the same for Course B Certificate and quiz to activate Course C.
Repeat through all courses.
The issue, I suspect, is that unless you have all Users working through the Moodle, you won't be able to track completion. So the response is how to be able to keep them coming back to Moodle, thus keeping your tracking in place.
Of course, this kind of structure is difficult to implement if Users can select different courses to undertake and can make their way to the end goal by any number of paths. In this case, you may want to use one single Moodle Course with a Choice activity at the end of each section instead of a quiz. As they select their path, make a choice, a record is kept of what their selections are so gives you an idea of what Certificates you would expect to see.
Another alternative is to find out if the external sites are LTI compliant, then you should be able to use the Moodle LTI implementation to connect to the courses. This SHOULD allow you to track your Users completion status considerably more easily.
I suspect there are other solutions, but these are the ones I am likely to try first.