The best way to farm transmog in old legacy dungeons is to have them all in their own instance and either try to sync it up or do it the messy way which I feel is faster and just auto run each character and keep swapping screens while blasting everything.
The reason for this, you get the same loot in each dungeon if you have 1 or 5. So breaking it into 5 separate instances is 5x the legacy loot. The problem you run into now is you can't share the gear with each other.

When I ran 5x druids through a dungeon all on their own though, it was quite enjoyable because you can get close to if not fully completing sets in just 1 run because your essentially doing the dungeons 5 weeks in a row.

You could go through the original method, but your severely limiting the potential overall sellable loot. End result, you got options.