You are doing exactly the right thing. No matter what other sources might imply, companion (cert) tickets can only be booked using that portal at DL.com that you are using.

You could experiment with dates a few weeks before and after your desired dates, just to see if there's a pattern you can discern regarding availability.

DL is aware of peak travel patterns like spring break, so if you ever find a date that works for you, my suggestion would be to book it immediately.