Well, I took the test on August 26 (Original window was between August 23 - September 12). I got the call on September 3rd about the test invalidation. Then, on September 29, I received notification of my re-test with the new window being between October 4 and October 24).
I gave it the morning of October 4 (didn't want to wait any longer) and am waiting for it to move to Completed (pretty confident it should go through without an issue this time, seeing as I used a different machine and my webcam was on throughout and I didn't see that cross on the webcam thing that I saw the last time).
My recommendation is to use a laptop or something with an inbuilt webcam - my mistake the last time was using my desktop with a USB webcam, which based on my research after the event, seems to be hit-or-miss for a lot of users giving the test. Also, make sure you have given your browser all the appropriate permissions as well; in my case, I used a Macbook and Safari the second time around, because that is exactly what they specified in their letter as well.
As a bit of positivity - the first time I gave the exam, I got 19/20 and I was baffled about what I got wrong. This time around when I went to retake it, I scored a full 20/20 and even though it's silly, it made my day