I think your use of the term "braille reader" might be causing some confusion. I know you use brltty. But do you use its text-to-speech output, or do you use a refreshable braille device that moves little pins up and down to form braille cells? If the former, I'd suggest referring to brltty as a screen reader.
Also, do you run brltty on a Linux text console, or in a terminal window in your Sway session?
Wow, I underestimated your seriousness about adapting to alternate output methods. Did you have to buy that braille display at your own expense? As I'm sure you know, they're expensive. How recently did you start learning braille? Has it been a challenge for you to learn to read it with your fingers?
I bought a cheap used one off of eBay, it wasn't too expensive - a few hundred bucks. I know that nicer ones can get up there, though. Learning braille was an unusual challenge, but I didn't find it especially difficult. It only took a couple of days to become reasonably proficient with it. The braille display I ended up with is pretty nice despite its price tag, it has a good finger-feel to it and has a nice set of basic features.
The most difficult thing for me would be learning advanced levels of braille, which involves memorizing shortened forms of many words, but I reckon I can get away with just using long-form for a good long while.
Also, do you run brltty on a Linux text console, or in a terminal window in your Sway session?