The transports are not available any more. I do not know if that means the laser can't be replaced but they wear out and I believe the symptom is skipping on ever more discs and with ever increasing frequency.
Cleaning the lens very carefully is a good idea. Rubbing alcohol will likely leave a cloudy residue behind, which you can check by putting some on a clean mirror. I would use 99% isopropyl mixed with distilled water in a ratio of 3/4 alcohol and 1/4 water. A cotton swab can be used, as I said, carefully.
A good alternative is a BDP and a BDA of any vintage and you can rip CDs with any computer drive to lossless files. It's one nuisance per disc against future convenience. If you have a working player now, there's time to plan your next move. Enjoy. 
Cleaning the lens won’t help. It will need an overhaul and possibly a new pickup assy. Like so many boutique manufacturers, Bryston used a pretty unremarkable transport in its pricey machine. As a result, very few specialists bother working on them and when they do, it usually costs the customer dearly.
Like Krell, Densen and all the other boutique makes, Bryston will blame the manufacturer of the drive – Philips no longer makes it so we don’t take responsibility for it. But It’s as lame of an excuse as anything because Philips wasn’t the one who took your money.
I am sorry to tell you this but you won’t find what you are looking for on this forum. Bryston didn’t make the mech nor do they know how to fix it – they would need to understand how it works first.
The good news is, this mech was used in hundreds of CD players and a working one could be sources from one of those players so you might want to look into that.
