Dang, there's enough old wood and stick debris laying on those trails to make me queasy lol. More than once I've had a branch like that lodge in my undercarriage (by some miracle though I've managed to avoid having a brake line or something else ripped off, though a buddy of mine had one get stuck in the gap between his aftermarket tube bumper and the tailgate, damaging the tailgate)
Anyway, ok, so your axle should've had the later style seals in it originally ('92-'93 was the changeover year).
I recall there is an axle seal that actually presses down into the back side of the spindle... It's been a long time since I did mine, but I think you have to remove that seal for the others (older style) to work correctly (or maybe it's the other way 'round, you leave the pressed-in one there and not use the V-groove seal, I forget which). Whichever the case, the press-in seal AND the V-groove seal can't be present at the same time (the V-groove seal would have no place to go other than get crushed by the metal surrounding the press-in seal).
It was many years ago (back around '96 when the axle was still under my Ranger) that I lost a set of bearings to water intrusion after going through water very much like in your video (this was with all the factory seals still in place). A couple weeks after that they started humming real bad... Upon inspection they were fully covered in that rust goo and the races were badly pitted.
I switched to the early seals like I showed above before the axle went under my BII, and after this trip below I examined them after I got home and found no trace of moisture (there were about 8-10 puddles in a row like this, coming out the Tahoe side of Rubicon):
Thing to do is slather that lip seal with as much grease as you possibly can. Lay it on thick, fill the whole back cavity. This will further help prevent water getting in past there.