My English Axle seems to have a lot of movement at the hub before it "engages" when I move it back and forth, and it's also making a clicking noise when I turn the hub. Is this normal? What would be causing it?

Here's a video but you might need to turn the sound up to hear the clicking.

Backlash in the diff looks ok noise all I can hear is noise through the diff and drivetrain hope that helps

as said backlash doesn't look excessive. not sure about the noise though, mine certainly doesn't sound like that.
has the diff been out and not filled back up with oil yet? as that would make it noisier.

Have you got bolts sitting in the front flange of the dif? I've done this before to keep then "safe". I forgot they were there and nearly smashed the nose of the diff trying to push it out the shed! Seems like something like that. Unless there's a damaged tooth in the diff

The front of the diff is bolted to the prop. The clicking is definitely from the diff, like teeth engaging. It just seems very clicky to me. It's been sitting for a while so maybe half the gear has been sitting out of the oil? I'll check the oil level when I can.

Good to hear the backlash doesn't look too bad.