However, a similar feature is available in Cache Rules (beta) regardless of plan level. What you need to do is replace your Cache Everything Page Rule with a Cache Rule that only matches requests without the relevant cookies, then set it to “Eligible for cache”.
When incoming requests match...
Hostname equals "example.com" << your WordPress hostname AND
Cookie does not contain "my cookie prefix" AND
Cookie does not contain "another cookie prefix" AND
URI Path does not start with "/wp-" (let default cache apply to `/wp-admin`, `/wp-content`, etc.)
and other conditions as your installation may require.