An update: today I was able to see appointments available for rescheduling! After checking daily for the past weeks, today I was presented with a few dates and time slots. Unfortunately these slots are all in between the 20th (my original interview date) and 28th April, during which I will still be traveling, so I will keep checking.
But it is good to confirm that this rescheduling system does actually seem to work, and you no longer have to miss your original interview to reschedule. I am not sure why they released some appointment slots now, but assume they will do this every so often.