After multiple respiratory, cardiac, and other organ tests, pulmonary fibrosis was ruled out as cause for my sob. Reduction of propranolol usage has helped somewhat, but not completely. What next?

Reduce completely? So you've had a thorough investigation, all of which has been negative so far. Reducing your propanolol has helped but not completely. I'd venture to ask why not stop it completely then and replace w/another blood pressure medication. Surely there are others you can take that won't affect your breathing! if you need a rate limiting agent, consider Diltiazem or verapamil, which won't affect lungs.
Why propanolol. If a reduction in propanolol helped is it necessary for you to be on propanolol at all? Discuss with your doctor other options and see if you can get off this medication completely.
Have they. Done a methacholine challenge test? You might have a form of asthma. That would make since as propanalol would make asthma worse.
Exercise. If cardiac and pulmonary reasons have been ruled out and beta blocker induced(propranolol)asthma ruled out, deconditioning could be the cause so gradual exercise should improve.