You’re probably sorted by now, but when I replaced the alternator on my FZJ105 it was clear that it wouldn’t come out of the top or bottom of the engine bay, so I took it out the side. The 105 has a plastic wheel arch liner that is very easy to remove (it’s in two parts), so I removed this and disconnected one of the power steering pipes and out it came.
On an FZJ105 the alternator is on the passenger side, on a HZJ it should be on the drivers side; you may be able to use the same approach, as long as the steering shaft doesn’t get in your way. Another option would be to move the A/C compressor out of the way, whilst still keeping the pipes connected so the A/C system remains intact.