As I understand it, checking your additional verses with the copyright holder is not just a courtesy, it's the law. This is from the FAQ at the US Copyright Office. Adding verses is considered a change.

How much do I have to change in order to claim copyright in someone else's work?

Only the owner of copyright in a work has the right to prepare, or to authorize someone else to create a new version of that work. Accordingly, you cannot claim copyright to another's work, no matter how much you change it, unless you have the owner's consent. See Circular 14. A .pdf file

I don't know about the details of application once permission is obtained. It seems like the exact notes, payments, etc. would be negotiable, but this is what lawyers are for.

Copyright is secured automatically when the work is created, and a work is "created" when it is fixed in a copy or phonorecord for the first time. If you want to register it just to be sure the fee in the US is $30.