What exactly is wrong with your immune system? What test results do you have? Have you actually measured your adrenals with and without exercise?
My immune system sucks too but I doubt you have the same problem. I have pan-CD3 lymphopenia. The only "hack" I found recently is ibuprofen 100mg 5x/day. It keeps the fatigue at bay and enables more exercise. Most people think of ibuprofen as an anti-inflammatory but it also boosts TNF in the periphery.