Since there are so many dungeons, I think the idea of a megamall with NPCs lined up one per dungeon is probably off the table, if not for performance reasons then lore friendliness issues.
So how might dungeon sets be sold Bind-on-Pickup for AP in a somewhat lore-friendly way?

Suppose there is one merchant for each Alliance territory. Say for the Ebonheart Pact, her name is Ebby.
Ebby starts at one of the gates, walks a day-long circuit passing through every town in Cyrodiil, not just towns near her Alliance. Her circuit starts at one gate, ends at the other.
Each time she's on a circuit, she has a full set of gear from one dungeon in her Alliance territory.
So today it might be Blessed Crucible. Once she reaches her end point she disappears for a bit to refresh her wares. So she might come back with Ruins of Mazzatun.
To make things more interesting she could start running if there's combat nearby, shortening her route (but also refreshing her wares earlier).

For dungeons that are not properly in any particular territory, it could be handled by a different merchant who walks a circuit in the Imperial City passing through all the District banners.

You might ask, "Should dungeon sets be sold through a vendor? Wouldn't that make people stop doing dungeons?"
That's a great question. Let me get back to you next week. I'll ask the Golden Vendor how she handles it. I need to pick up a Monster Set helmet from her anyway.