I asked my Dr. about beta blockers for a medical condition I had a few years ago (that's the reason I knew something about them ) and while she isn't a dive-medical expert she said to me, and I quote, "I would find scuba diving on beta blockers inadvisable". Upon asking follow up questions her opinion was based on beta blockers effectively lowering (damn, I can't think of the English word right now..) "inspanningstolerantie"... I guess literally translated it means "tolerance to endure exercise". It had to do with the limiting effect on how high the heart-rate can get. She described exactly what the OP said, which is that high levels of exercise, like jogging, can cause you to feel exhausted. Her opinion (and again, she doesn't have a dive-medical specialty) was that feeling exhausted on scuba probably wasn't a good idea.
I was using Atenolol, a beta-blocker, at the time of the incident. I have since switched to a calcium blocker. I need to find out how this may effect the situation. I agree that the Atenolol contributed to my IPE hit. I have had A-fib 3 times in 7 years and the last time I had to be converted by shock. That's the only reason I was put on that med. I'm doing more research to see if I can drop all meds for this condition since it does not happen very often.