I usually appeal directly. I will try your method and see if it worksIn my experience the best thing to do is submit the requested doc via form for the support inbox
then click support links from email (they send a reply that they're reviewing ...2-3 days etc.)
wait a day (they block chat for the first 24h)
start chat support if it hasn't already been pushed through on support inbox.
get the account back within 48 hrs.
It's usually a 3 day downtime every time it gets flagged though.
My ads are usually GH or BH so it's more difficultIt depends more likely to what kinds of reasons your account disabled.
You can't speed up your appeal rates actively.
If the fb support guys happened to be enthusiastic, you will get review quickly.
There is less thing you can do.
If you would like a try, next time you appeal, be more sincere.