At 30% this is getting close to heart failure. The heart can recover without exercise and what you don't want to do is make your heart start to compensate and become even weaker due to exercise. If your Cardiologist has asked you not to exercise until the 30% rises, he has very good reasons.
I remember reading a case of a young girl in England who had heart failure. They couldn't find the reason for it and she was on a transplant list. Luckily a donor was found and they put the new heart in tandem with hers, rather than removing it. They stopped her own heart and left her donor heart running. This obviously pumped blood through her own heart, but this wasn't beating. Over the weeks they were astonished because her own heart returned to normal size etc. They stopped the donor heart, and restarted her own heart. After a couple of months they felt confident enough to remove the donor heart and years later she is still normal. It appears that the heart recovers quicker in rest.
A few years ago in the UK, they started to insert LVAD (left ventricle assist devices) into the bodies of patients with heart failure, to give them more time to find donors. Some patients made a full recovery because the heart had so much less work to do, thanks to those tiny pumps.
My ejection fraction rate has been in the 30% range, then raised to close to normal, then seen if fall, and raised again. Currently it probably is close to normal. In my opinion, determining the EF is a slippery slope.
What has led to your heart problem that required the medication?
Coreg, or carvidilol which is the generic replacement, is a very powerful drug. It is difficult to take, that is why you are being given a very small dose twice a day. It makes you very tired, and slows your metabolism. However, your body will get used to it, and the drug has properties that allow your heart to heal the heart. Once your body is used to the drug, often it is double, then doubled again, perhaps a third time. I took 50mg a day for a number of years.
The drug raised my EF fraction to almost 50%. Unfortunately, I had another heart blockage that led to bypass surgery, and now I don't have to take the drug. However, I think it kept me alive for a period of time. I wouldn't give up on it.
That being said, I refused to quit exercising. I did quit weight exercises, stopped jogging but walked and did aerobic work at the fitness center, and think that my activity helped to raise my EF fraction, and the nurses all told me I sailed through the recovery of bypass because I was fit.
I would expect to feel lousy because of the Coreg, but anticipate good results. I'd challenge the request to stop exercising. There may be a really good reason to stop, but I'd sure make it a conversation point. I'm not a health professional, but I've been in your shoes.