I would get your 95% guaranteed tenure before moving on, if I were you. All administrative jobs (in my state at least) are considered "at will" employment with a new hire letter every year and you could be let go at any time for any reason. You may have one of those iron-clad, can't-be-fired-despite-incompetence jobs but you are only protected until the next dean or president comes on board. And you may be someone who does an excellent job by all accounts but takes a principled stand against a new policy of a new administration and you would be out on your ear - just like 99% of the jobs that don't involve tenure. Moving from a tenured position to some administrative post at your current institution might give you the protection of returning to teaching/researching work if you rub the wrong person the wrong way.
Working in study abroad and/or with international students can vary widely depending whether you are a one person office or have a staff of 20 plus. In small colleges, you will wear many hats where you may be doing everything from filing, data entry, and requesting checks, to heavy loads of student advising, to negotiating contracts with the big wigs of a premier university overseas and managing crises across an ocean or interpreting for an international exchange student who has been arrested in your town for shoplifting. It is certainly never, ever a dull moment. And many in the field will not be pried from their jobs in study abroad. It can be a calling but most people find it incredibly rewarding. I know very few people who actually work a 40 hour work week, it is usually more like 50+ hours with some weeks being 24-7 if you have to evacuate students from your program in the latest location to have natural disasters or political unrest.
In larger university systems, the positions get more specialized and the latest new position being advertised seems to be for a job called a Health and Safety Risk Manager, which involves everything from making sure housing on the study abroad program has smoke alarms and deciding whether Clery Act reporting requirements apply to a university program in another country and lots of things that involve protecting the university from lawsuits by being able to show that you planned for every possible thing that could ever go wrong with students studying abroad. But there will be a wide range of positions ranging from advising, to recruiting students, to admission work, to program management, to curriculum development, etc. etc. I would suggest going to the NAFSA website
http://www.nafsa.org/knowledgecommunity/default.aspx and signing up for the SECUSS-L listserv and go to the archives to have a look at the variation in job descriptions posted over the last several months.
The field of international education has becoming more "professionalized" over the last two decades with more and more of the top jobs requiring a PhD or master's degree and new "standards' being developed for every aspect of this enterprise. For information on standards in the field - go to the Forum on Education Abroad -
http://www.forumea.org/standards-index.cfm. And yes, "assessment" is a word you will hear often. Since you have served on a study abroad committee, you should have people you can go to and ask about such things.
About teaching occasionally, I would say that in my experience unless the job description mentions teaching responsibilities, a candidate for a top position who mentions wanting to teach a course or two is like waving a big red flag for the search committee. It is not that it won't be possible but that can be a sign that the applicant has no real idea of what is involved in managing a study abroad office or program. I can tell you that no one will look favorably on doing anything like prepping for classes or grading during the 8:00 to 5:00 business day. That is something you would have to do "on your own time" but that sounds like what many here do anyway, prepping and grading on weekends and holidays, it is just that your official office hours are 40 per week, not the 3-5 hours of posted office hours for a faculty position. You basically lose the flexibility of work hours that is one of the perks of being a professor.
But as they say, your mileage may vary and if you look at some job descriptions on SECUSS-L you will see everything from recruiter/sales jobs with quotas to meet at a study abroad organization to high level administrative positions at a college or university where you are providing leadership in a very dynamic and visionary position. Good luck!