Honestly, I wouldn't "ask" for anything. Sure a stress echo would be an appropriate test but you need to go in there with the only focus is sharing your symptoms and asking for them to find the cause. Doctors don't like to be told what tests to run or what patients think is wrong. They want to be the doctor and be in control (we all know how big their egos are---lol)

You need to show them what is happening. I have experienced the same thing as you and literally took my pulmonologist to the stairwell to 'show' him what was happening. It was an eye opener for him. The cardiologist had me step up/down off the foot stool at the end of the exam table...which produced the same thing and he could 'see' what was happening with my heart rate and breathing. He simply hooked up the EKG while I repeated the foot stool thing and sure enough, he could 'see' the Dx of inappropriate tachycardia. He helped him to further Dx my autonomic dysfunction.

You should also document as best you can what things produce what results (what exercise causes what symptom) and write them down. Experiment with things so you know how to describe exactly what is happening. Take your heart rate during these episodes and even your BP (most machines do both). If you have low BP (autonomic drops), then your heart rate will increase when your BP drops (compensatory action) and this combo makes anyone short of breath.