Display a certain question after every 2 question blocks?

Hello,
SITUATION:
I'm trying to make a survey in which participants fill out several questionnaires. These questionnaires are displayed as blocks. These questionnaires (blocks) are Randomized (displayed in a random order), which basically shuffles the order in which they are given to participants.
MY PROBLEM:
I need to show 2 questionnaires (blocks) at random, and then insert a specific question after every 2 questionnaires. So, I need a way to Randomize all the Questionnaire blocks, count off when 2 questionnaire blocks have been completed, and then insert that one specific question after two questionnaire blocks have been completed. If you prefer visuals, see the attached diagram for a simplified illustration of the problem.
CURRENT WORK:
In the survey flow, I currently have metadata to track when two blocks have been completed. Basically, after every questionnaire, I add +1 to a Count metadata variable. I was planning on using this Count variable to keep track of the number of questionnaires completed, and then somehow show participants that one specific question when the Count variable hits 2, 4, 6, 8, 10, etc. (which effectively would show them the question after every 2 questionnaires completed).
However, I cannot figure out the most efficient way to display the specific question after every 2 questionnaires. I think I could use Branch conditions, but there are nearly 100 questionnaires, and it would quickly become very unwieldy to insert Branching conditions for each questionnaire.
ASK:
Do you have any thoughts on the most efficient way to display this one specific question after every 2 randomly-selected questionnaires? Ideally, the solution wouldn't involve Javascript.