WP Engine 502 error when publishing with 300+ subscribers

On https://manor.pennmanor.net/ (Subsite of a multisite network) I can create a new post and publish just fine when I select "Do not send this post" from the "Subscribe by Email" box. However I was try to publish with email notifications it spins for awhile and then ends in a 502 error. I asked WP Engine about it and they said any script which takes longer then 60 secs is killed. It looks like that's what's happening here. Any suggestions on how I can get email notifications working without hitting that limit? I do want the emails to go out immediately however maybe someway to handle them as a background process? Or maybe there is something else going on here.