An update, because seeing update from the users before me helped a lot!
I clicked reschedule on my appointment on around the 25th of May. Daily since then, I have checked the website and there were no appointments available, and I was getting a little stressed. Then, upon checking today, I was able to rebook and appointments were available. All were on the 17th to 20th of July, and with several timeslots to look at each day!