I don’t know what you should do. I think the first thing would be to identify why it is falling apart. Dry rot is a fungus disease caused by moisture with poor air circulation and periods of heat changes. From things I have read, you pretty much have what you have, it’s not going to get better; you can only stop it from getting worse. Deteriorating leather (red rot) usually recommends lanolin and neat's-foot oil. There is Renaissance Wax, I’m sure it would help but if a better solution came along it might be problematic once applied. Certainly would not be a bad thing for the wood. Here are a couple of links you might want to look at.
http://www.woodfinishsupply.com/RenWax.html http://www.philobiblon.com/pressite.htm
There is a collection of essays "Caring for your collections" by Harry Abrams, but I have not read it. Maybe calling some conservators and seeing what they would do??