Hi Sean, as an editor I run permissions for authors. It’s a case of contacting each right-owner (author or publisher) where the quotes are not deemed public domain, and provide them with context for approval. You can do this yourself or I’d be happy to quote for the work, if you’d like to contact me directly? My email address is email@example.com.
It’s always sensible to follow due diligence in submitting your first draft of your book to an editor by making as fool-proof a copy as possible for you because first, it is your own creation, and secondly, a horrid draft sent your editor can end up frustrating both you and him or her. Make your own corrections to the extent you can, so that will make the job of your editor that much lighter and the end result would be a lot more effective.