I too have this same problem but I believe it is iron related. I have read that runners can become deficient in iron and still not be anemic when tested. However oxygen is transported throught the red blood cells and the red blood cells are nourished by iron so this makes since. You might try stopping exercise for a while and increasing your lean red meat along with Vitamin C, like from orange juice in order to help the uptake into your system. This seems to work for me.
From your description of gradual worsening over several weeks, culminating in persistent, unremitting dyspnea, the diagnosis that first comes to mind, especially if your chest x-ray is clear, is that of recurrent pulmonary emboli, with or without pulmonary hypertension. You state that, 'Heart/Lung problems have been ruled out through much testing.' You may want to confirm that your doctors have completely ruled-out pulmonary emboli. It is a condition that can be very insidious. What you describe is not the result of a low carb diet, alcohol consumption or overtraining.
If emboli have been ruled-out, interstitial lung disease has been ruled out by physical exam and high resolution CT scan, and metabolic disorders of muscle have been ruled-out, your next step should be to have a stress exercise test, possibly to include an echocardiogram. Preferably this should be done at a center with expertise in exercise physiology. Two such centers are: