Hello!
Congratulations on the AC invite, that is fantastic news!!
I would try not to worry - this is a relatively common issue, and firms are generally very understanding as long as you let them know promptly (which you have done!). I had a similar issue when I was invited to the
Reed Smith AC last cycle as I couldn't attend any of the original dates, and was able to move to a later one with no issue - as long as you are polite and flexible, it shouldn't count against you at all.
Hopefully they should come back to you with a new date soon - you have done everything right here, so try not to panic
Best of luck with the AC!