Sending a 410 responses for a page that no longer exist should make Google stop crawling for that page.

The site I am working on has been recently migrated, and very little of the content was migrated.

I've already turned the existing content into 301 redirects (the content that is on both the old and the new site), but now I would like to flush the old content from Google's memory by placing 410 responses in it's path when it returns to crawl for them and finds a 404 response.

However, I asked our CMS host about it, and they said that our CMS does not support 410 responses. Is there some other way to post a 410 response, like making a dead link 301 redirect to a page that a 410 response in the form of a meta tag?