Whaaaooo... yeah, that's alotta wiggle there.

What's the situation with the front diff's fluid? Have you drained it yet to see if it's got a fancy metal-coat sheen?

If it vomits out chunks of spider gear, you've found the problem.

Because it appears that the half-shafts (diff to the wheels) are remaining stationary when the input shaft is rotated back and forth on its free-play; and if that's true, I'd estimate the problem is localized inside the front diff. Spider gears are toast, or the ring gear and pinion aren't engaging correctly anymore, can be caused by the crush sleeve getting... well... crushed. I'm sure there's other things that can cause that sort of free play, hopefully someone more knowledgeable can jump in as well.

The fluid condition in the transfer case... Ya know, I just have a hard time thinking something could go wrong so badly to make that sort of dramatic free play in the transfer case and it would still run smoothly (in 2WD with the front driveshaft removed). With the full time 4WD, it's all gotta spin, so I would have assumed if something got ground up, it'd let ya know with a lot of racket when you drive it.

Thanks for posting a video. I think the condition of the diff fluid is the only thing that could confirm definitely if the front diff is definitely blown up without doing any more exploratory surgery.

I'm certain there's some Toyota 4x4 exclusive shops around Calgary that would know in a moment what the issue is. It really pays to have a guy who knows specifically about this particular vehicle.