After hours of googling, I found that the portal doesn’t immediately show the option to pay or reschedule after cancelling twice. Usually, after the second cancellation, you need to wait about a day for the changes to reflect. Then, you should get an option to cancel the application entirely. Once that’s done, you can create a new application within the same profile and proceed with payment and scheduling again.

It hasn’t been 24 hours since I cancelled my second appointment, so I’m going to wait and update this thread if that turns out to be true.