Do I need to replace cupped/curled plank sheathing in my wall?
Mold is rot.  Bleaching was smart.  A Mildecide is what you want.  That siding I believe is called shiplap.  Incredible, tough, tight siding.  I am not sure about the other layers, kind of confused.

You need ventilation through or between the walls to completely stop the rot and mold.

If you could draw a simple 'cross section' of your home's walls, that would help me.  Dry rot is tough to 'see'.  Someone that understands what to look for should be right there with you to go through your home.  I've hired these home inspectors who work for you not the bank.  And I've built 30 custom homes!  I don't know very much about old construction and these inspectors are trained to look at old, aging structural members. They know about the old construction techniques.  Worth every cent!  I hired one for $120 to go through my 4000 square foot log home to check the foundation and other things such as proper blocking, heated floors, roofing, septic...I learned so very much in a few hours and I was already considered an expert! 

Dry rot is like a cancer and you really want to know what is rotting and what is not, but you have to have an expert right there.  I would not take out shiplap unless there was dry rot.  Please let me know what you find when you call a private home inspector.  This definitely warrants a few more calls and appointments before making decisions.