Apartment Going Back On Signed Lease

I recently moved into an apartment complex and am utilizing their 30-day guarantee policy to transfer to a different unit that has recently become available. I signed a lease, agreed on a move-in and move-out date, and was prepared to pay the new rent and deposit. However, when I tried to access the payment page, I was informed that my new apartment was no longer available on my move-in date because the current tenants had extended their lease and changed their move-out date. I was told that I needed to choose a different apartment or face penalties for transferring outside of the 30-day guarantee.

The new apartment is now available on the 4th, which is 8 days after the 30-day guarantee period. When I inquired about the change in the move-in and move-out dates, they explained that the current tenants had extended their move-out date and that "sometimes this happens."

My question is: since both the apartment complex and I signed the lease agreeing on the move-in date, can they legally state that I can no longer move in and that I must select a different apartment? This situation seems to be an error on their part, and they maintain that there is no way around their 30-day policy. They also did not inform me of the change until I reached out to them about my inability to pay. This makes me believe they were not aware that the apartment was no longer available on the agreed-upon date. They are insisting that I cannot move into my new apartment without paying the transfer fees or selecting another available unit. This situation seems questionable, and I need some advice on how to handle it.