I'd double check with your vet on any exercise program to build muscle. My mare has what my vet calls "low grade heaves" and he encourages my riding her. We just do lighter/easier workouts when she is having coughing episodes. So much will depend on what your horses respiratory capacity actually is.
As others said, there is no cure however, management can make a huge difference. Keeping your horse outside as much as possible (but in a low dust area) and soaking hay can really do wonders for a heavey horse. Also, when your horse does need to be in a stall, trailer, etc. moistening any bedding can help keep dust down and prevent outbreaks as well. Keeping any riding areas dust free is a good idea also.
Heaves doesn't have to be a career ending diagnosis. My girl still competes in both traditional shows and competitive trail rides with no problems. She has only had flare-ups when our lovely Michigan weather has required her to be stalled for multiple days at a time.