I know nothing about the BW4401, but my NP241 was also grinding and jumping out of 2H into neutral. I have yet to tear the old one apart, but as far as I know both the 4401 and 241 have a chain drive inside, so best case scenario you have a spent chain and/ or worn gears and bearings.
From what little I just looked up online, it looks like the 4401 has an internal electronically actuated clutch coil that can also go bad. However from my understanding this clutch coil is used to engage 4wd, so given your symptoms I'd venture a guess that the coil itself isn't the issue. But depending on your own time and financial resources, it may be quicker and cheaper in the long run to purchase a rebuilt unit as Chris suggested and save yourself the headache of a t- case rebuild