I had the same problem with JoH. The zone and the story is fine, and I have had armor drops. Yet, the schematics for both the Haven and Undercroft chests have never shown up. I haven't bought SotQ and from what I've seen so far, I have no plans to.
I've tried much the same as you did, OP. This is what I've tried so far for JoH:
1) Uninstalled the DLC
2) Deleted the Item folder manually
3) Deleted my "Merged Folder" from my mods manually
4) Repaired the game
5) Made sure the game was fully patched
6) First tried installing it from the BioWare site and not from Origin
7) Then tried going through Origin via the download tab in Game Details.
8) Did not add a single mod
9) Stayed online and made sure I was connected to DA servers
10) Played for about about 45 minutes in the new DLC before heading back to Skyhold
11) Tried a save at Haven with the same character
12) Tried an end-game save from my first character
13) Rolled up a brand new character
14) Tried a mid-game save from another character
15) Tried the above with my first character
16) Then repeated steps 1-15 again, in various different orders and a few different characters. As well as different class/race combinations. For about 5 hours.
Nada. Nothing. No dice. The only thing I haven't tried yet is reinstalling the game entirely. I don't know if Patch 8 addressed this, but it does tork me off a little. I paid money for the schematics as well as the rest of the DLC content, and it has never worked. I've been holding off on DA:I until this is fixed. I hope it does get fixed in a way that doesn't involve the player having to monkey around to this degree.