Prefer member variables over function scope statics

[cleishm]

Move function scoped statics to class members, as the static is shared for all class instances.

[cleishm]

It also wouldn't hurt to clean up the member variables in the class, as they're declared and initialized in inconsistent ways. However, I tried to keep changes minimal for this PR.

• Can remove all the volatile markers, as all these member variables are protected by the mux.
• Use either inline initialization in the class definition or initialization in begin. Currently it's a mix.
• Add doc comments or remove them for internal variables. Right now some have them, some don't, and some have empty blocks.