I don't have any creative suggestions for you. But I experience the "general overactive stress response" you mentioned. (I also have little tics that come-&-go periodically.) I've struggled with this my entire life. After a while I think my body simply no longer knew how to function any other way. So at this point in my life my body feels like it's churning 24 / 7.
I don't take anything for what I experience. And, in fact, I'm a black tea drinker. So I get caffeine from that as you do from coffee. Perhaps I should give it up. But it's one of the few pleasures I have left in life. Back when I was seeing a pdoc he suggested writing me a prescription for Klonopin. He said it would smooth out the churning. I decided not to go that route at the time although, occasionally, it occurs to me perhaps I should reconsider. (I probably won't.)
Here are links to 5 articles, from PC's archives, that discuss ways to alleviate anxiety, just in case you haven't already read them:
10 Things People With Anxiety Need to Do Every Day
Eat Right To Ease Stress
9 Ways to Reduce Anxiety Right Here, Right Now
15 Small Steps You Can Take Today to Improve Anxiety Symptoms
Top 10 Lesser-Known Self-Help Strategies for Anxiety