This is a very very hard limit - is there any way to increase it?
I believe they just changed this, reduced the limit due to a few accounts abusing it. I’d reach out to support and see if they’ll do something specifically for your account.
Why would you need to publish the site more than every minute?
Just to be clear, if you are adding/updating CMS items with the live API endpoint, those are published under the original API rate limit of 60 requests per minute.