A few of the old outfits are locked behind boxes that only come from running random scenarios which, as far as I can tell, don’t exist anymore. You can run a character into the shrine for a quest once (woo) but it seems a one off.
Anyone know if this is true or am I mistaken/there’s a work around?
You have to be more specific. What random scenarios are you talking about? There are Heroic scenarios which are repeatable same place the raid finder is. 
Other than that the PVE quests but again your going to have to be more specific, what items specifically where you yrying to get?
They do all still exist. If you wish to run one of the Pandaria scenarios, then head to the Vale of Eternal Blossoms and head to the Seat of Knowledge (which is at the top level of the Mogu’Shan Palace).
Lorewalker Cho will have quests you can do for the scenarios.
You can queue for a regular scenario with Lorewalker Fu.
If you wish to do the heroic scenarios, then speak to Lorewalker Shin.
Also, the NPC in your respective Shrine will have a quest as well.
I just did the initial quest from Lorewalker Cho (The Warchief and the Darkness) and received a rare quality cloak from the chest reward.
I then did the heroic scenario quest (Heroic Deeds) from the NPC in the Shrine and received an epic quality helm from it. This is a one-time quest.
Mmm. I know about where to queue.
The problem is you only get a chest from either the one time quest (heroic deeds), or for queuing for a random heroic - not a specific one. And I think (or am trying to find out if) the ability to queue for a random heroic has been removed or if there’s another way to queue for one and get it.