Am I completely overthinking this?
If we are talking about emotional stress coupled with a slight increase in heart rate, I would not be concerned about doing exercise. Quite the opposite -- I think a quick jog around the block can do wonders.
The key is to be able to do the exercise without bringing additional stress.
For example, I might suddenly get hit with a feeling of terrible loneliness, even though I am with my partner or among friends. Instead of telling myself "hey, listen, you are not alone, stop feeling lonely!", I tell myself "this is a memory of a moment where you really were left alone. poor me. thank you for reminding me of that past horrible moment, now that i am fully capable of giving it the loving attention that it deserved back them but didn't get".
This process takes some effort to learn, and accepting that you are still learning and not already perfect at it is a key part of the practice. But even small moments where it "works" in my experience finally actually resolve stored up emotions, so each time an unpleasant emotion comes up it hits me less and less. It is not important to understand exactly what triggered it, or what the past traumatic memory is. Do not ask yourself, just be, and open your heart.
There are many different descriptions of techniques. The one I like the most is "Feeding your demons" by Tsultrim Allione.
1. Have things to look forward to.
2. Pay attention to nutrition, health, rest, breathing, exercise.
3. Meditate. Socialize.
4. Occasionally when anxiety grows, breathe, visualize yourself performing a repetitive yet fun activity (like swimming laps, chopping vegetables.. whatever takes focus). Your heart rate will drop and things will calm down.
Sometimes when your heart is racing, it's possible you just have pent up energy and you need to crank out some pushups and squats at 3am. Such is life.