While I have been post menopausal for quite awhile, i had the same issue. It significantly interfered when I was teaching classes at the gym. I never really found a total solution, except that sometimes just doing a milder form of exercise decreased a lot of the symptoms you describe. I am the exact same size as you; in fact, I weighed quite a bit less when I was younger and never experienced the loss of my period.
Why don't you decrease your focus on performance and just try to enjoy the ride when you are having PMS symptoms? If you slow down, this might increase the "good feeling," and decrease the physical symptoms. Stress about performance would definitely add to PMS symptoms, even physical ones, which I was the queen of. You certainly don't need to be "fast" when you commute. Riding at a slower pace will still get you the positive benefits and you won't have to "take the car" (though there is nothing wrong with that, either).
It sounds like you might benefit from some relaxation/stress reduction strategies, like yoga or meditation. Have you done any other type of therapy to deal with your athletic amenorrhea disorder? My experience has been that sometimes people tend to substitute one type of thing they can "control" for another, unless the root cause of your need to do this is worked on.