This treatment may kill your moss, but the once-per-week treatment I have found to not harm plants normally killed by Excel. I suggest starting at 1.5 ml of Excel per actual gallon (not tank rated gallons) and increase it by 1 ml / gal each week until all the hair algae responds.
I just got through my first week using the above method. My modifications included:
1. I started at 1 ml / gallon. My wife's favourite fish is in the tank so I had to be extra careful :-)
2. I also pulled some water out first and had it in a bucket in case I saw any fish in distress. It turned out to not be needed.
3. I didn't dose the entire amount in one shot. Instead I put in 5ml at a time using a pump to spread it around the tank. I waited a few minutes in between each batch to see if any fish showed distress. No distress.
Much of the BBA turned red two days after the treatment. It took a few more days for the BBA to actually disappear from the wood. I'm now in a holding pattern to see what BBA survives before considering another dose.
Otos, angels, SAE, red-lizard whiptail, and pseudomugils were all fine. Mystery snails also seemed fine. I can't tell if all assassin snails made it as I have too many to count, but I didn't see any empty shells.
I have a large assortment of plants and the only one that seems to have taken a hit is the water sprite. It didn't die, but a lot of yellowing leaves so some cleanup will be in order. I don't have any moss to comment on.
I can't believe it's taken me 3 years to find this approach, but I'm glad I did. Thanks @Deanna