Confirmed that this is the only method currently available with @mulby . Story on Analytics backlog, maybe also one for ORA2 team, to improve this experience. 
Suggest that instead of using images that show the csv files open in a spreadsheet application (where ordering of rows can be changed) that you instead show the csv files open in a text editor?
(but to clarify my original suggestion, the grade report does not contain any anonymized IDs, but it does contain the user ID, which you can compare to the user ID in the anon-ids report. So, if what you start with (prerequisite above) is a username or email address you can 1) download the grade report and find the user ID for that username or email address, and then 2) download the anon-ids report to get the anonymized and/or course-specific anonymized ID for that user ID. Since you were already giving two steps to get reports that then relied on no re-sorting, I thought the grade_report might be a useful alternative to enrolled-profiles)...