I like that I am not even in the top few oldest people on this board, even though I'll turn 60 in a couple of weeks!
My wife is a retired teacher who still volunteers in a public school classroom. Her best friend is still a teacher, and my sister is as well. What you say about today's administrators sounds very familiar to me. My wife is very happy not to have to deal with it.
I am probably close to being able to retire from a financial standpoint, but I have no short term plans to do so. Although I'm in a different field and have a short commute, I share many of your feelings about my job. I feel like I'm doing good, and I very much enjoy my co-workers. The work is interesting and engages me intellectually.
When I retire, I don't expect to travel that much either, but I can think of some other things I'd like to do if I had more time. Right now the appeal of those other things do not outweigh my enjoyment of my work and workplace.
One thing you seem to have going for you is that you didn't mention wanting to move. I suspect that you are happy where you live, given the commute that you put up with. A benefit of retirement is being more able to live where you want, but you don't seem to have that issue.
You also didn't mention the one thing I hear people my age usually bring up when they discuss retirement--health insurance. Maybe that won't be an issue for you, but depending on your age and circumstances, that could be a financial factor. I know it's something my sister, who is younger than I but can retire within a year or two, is considering. But you didn't mention it as an issue; so maybe that;s not a big consideration.
Given what I am hearing from you, I think you are not quite at the point of retirement. You may well feel worse physically within a few years, though, or maybe the administrative headaches will become less bearable. So while it seems to make sense for you to hang on for now, you might want to start making plans for how you will spend your time when you do retire (including time for exercise). I am sure that someone with your skills and experience can do some productive and rewarding things.
Best of luck!