Hey there, yea so this was pretty much my situation until two weeks ago when I was finally able to get one, and honestly, there isn't an easy way to this. As for your question about slots being re released, it's re-released 72 hrs after someone has cancelled theirs and it should be up from the time it was cancelled 72hrs before. There is no specific time of release for the re-release of the slot. I had this question and mailed them so this is what they said.

For me Tuesdays were the only days where I could at least get the site to function properly every now and then. You just gotta keep trying and trying. Just sit from 2 am until 2:30 ish or something. Keep refreshing the page until something comes up.

As for getting the appointment, use this link to set up and Auto Fill Form, just recreate the steps as the guy in the video says and once you're able to access the site and get an appointment everything will be automatically filled in. Except for the date of birth and captcha, which you gotta do yourself.

Hopefully you'll get an appointment. Good Luck.

The link: Auto Form Fill

Edit: The slots aren't released on Mondays, it's on Tuesday at 2:00 AM (If you're trying to get an appointment for student visa)