My solution for this is to add an activity that has an any criteria for availability--basically, this activity is not available until one of these two quizzes is complete. Then course completion is entirely dependent on the single activity. This will mean resetting course completion, which causes a few other issues but would resolve the issue. Then, if you have a new-new group and a different quiz for them, you reset the activity completion, add the quiz for an any condition and move forward. Not that I recommend this...but it would work.
I don't know what order your activities should be in but maybe make the assignment that activity?
I don't know what order your activities should be in but maybe make the assignment that activity?