OP wants to automate the email send but should not do that. Sending bulk automated emails is a big no-no.
There's a big reason why OP was fighting with providers to set up something to what amounts to marketing email without an unsubscribe link...because it's not something you're supposed to do.
I don't think you should automate talking to a recruiter, anyway. At most this system should just generate email body and allow OP to review and send it out manually.
That being said flagging e-mails coming from known IP ranges of those e-mail providers seems like a pretty good idea for ATSes to detect non-human spam.
There's a big reason why OP was fighting with providers to set up something to what amounts to marketing email without an unsubscribe link...because it's not something you're supposed to do.
I don't think you should automate talking to a recruiter, anyway. At most this system should just generate email body and allow OP to review and send it out manually.