We had a few staff request changing the order of the options of paging or leaving a voice message when they refuse a call/are unavailable - when they have a pager number listed.

I think this is a good option to consider. Depending on the department, user's may choose allowing callers the option of first leave a voice message followed by paging -  if the caller chooses to not leave a voice message.

Or instead of possibly confusing callers with the above option, another thought is to allow a user the option of not having a caller paging them from a normal call ("Call Dr. Jones, 'Do you want to send them a page') , but allow paging from a direct command "Page Dr. Jones".