@GraysAtlas,
Hi GraysAtlas. It seems that you have checked most of the possible causes(cardiac, renal, hepatic and vascular) of your symptom. There's actually one more category of edema, and it's called idiopathic edema. It is the diagnosis of exclusion.
After you rule out all the possible causes and you can't find any problems, doctors can name it.
In this case you can't diagnose it specifically, but for some women who are premenopausal, physicians can suspect premenstrual edema. Premenstrual edema is usually mild(sometimes worse), and selflimited, with a diuresis beginning with or shortly after the onset of menses. The edema is thought to be humorally mediated, as estrogen or prolactin. But unfortunately, there's not much we can do for diagnosing or specially treating it.
Also some drugs you are taking for MS caused or aggravated your symptom.
Doctors prescribe furosemide when patients are edematous, but hypokalemia and renal insufficiency are side effects that doctors are concered with. Please see your doctor and get checked regularly for potassium level and renal function if you keep taking furosemide. If your symptom becomes less severe and self-limited, observation with low salt, low carbohydrate diet can be an option. Hope you can manage it well with your physicians.