I don't know what to tell you about the box. The front bearing on the out put shaft is usually the first to go so you want to check that one and it's still in the case. Don't know about Clymer's warning about heating the case. I wonder how they think you are going to get the bearings out? It's not just Clymer's manuals that have weirdness tho, it's all manuals. I've found weird stuff in Ford Shop manuals.
Yep sounds like oil or grease on the clutch? Rear engine seal been leaking? Have you recently lubed the splines just before this happened? Take the clutch out. You can clean them and they usually work pretty good but the last time I over greased my trans splines and did this it was a ten year old clutch so I replaced it.
Oil seal? You found part of an oil seal? Would this be the trans front oil seal? A source of oil on the clutch if it is.