Not sure if this reply will be much help as I'm no Doctor and often wondered what my riding would be like if I wasn't on BP medication.
I'm 43 years old 3rd cat racing cyclist, like to think I'm fairly competitiive, and have had decent results at 3rd cat level from time to time.
I've often wondered why my HR max is so much lower than my training partners & have definitely convinced myself it's down to the medication.
They just think I'm super fit
I've often queried this with my Doctor but pretty much all he'll say is that if my medication had a detrimental effect on performance then we'd know about it as many athletes must be on the same treatment!
However I'm NOT on Beta Blockers as you are.
I'm on Amplodipine Maleate tablets which is a Calcium Antagonist.
Apparently these work by relaxing the Blood Vessels, so that the Blood passes through them more easily. Sounds like they should be on the banned list!
However, one thing the Doc did say was that he wouldn't put me on Beta Blockers as these would be likely to have a detrimental effect.
Having said all of the above, I believe there's a third type of treatment which is the best to be on if you're an athlete. Unfortunately I can't remember what it is and it's years ago since I saw the article.
At least as far as I'm concerned, I've been on these for approx 15 years and never had any noticable adverse side effects, just often wondered if I'd be a better cyclist without them.
Sorry it's not a definitive answer but hope this helps.