I was able to get it to work. I have the physical disc edition--I don't know that that matters at all. Unfortunately, I cannot be 100% certain what I did, so it may have been sorcery. EA support did not understand the problem, gave unrelated solutions, and did not attempt to replicate the problem as far as I can tell, so I tried to troubleshoot on my own.
1. I deleted the game from my PS4 (pro).
- I deleted the save game data too, although it probably doesn't affect this. If you have save data, maybe put it on a USB. I had to look up how to do this.
2. I reinstalled everything--DLC and update--EXCEPT Descent, and I did NOT let the game launch after the update file completed downloading/installing.
- First successful attempt: I installed the base game, Jaws of Hakon, and the "item content" upgrade DLCs with small file sizes. The game ran. Then I installed everything else and it broke. (I did not let the game launch after the update file completed installing.)
- Second successful attempt: I installed all the DLC except for Descent (and did not let the game launch after the update file completed installing). The game launched.
- Descent might not be the problem, but in 2/2 cases where I tried to install Descent, the game would not launch.
- I suspect the problem comes from Dragon Age Inquisition wanting to launch while the other DLC is downloading/installing. It wants to launch right after the update completes. I know that the first time I tried to install the game, the game launched after the update was completed, but after all the DLC was done installing, it would no longer run. However, I could be entirely wrong about this. The second time I tried to install the game, I did not allow the update to run, I installed everything, and the game would not load.
3. After installing everything EXCEPT Descent, I launched the game, played for a while, created a save file. I loaded my PS3 save game and played the Jaws of Hakon DLC. When finished, I crossed my fingers and downloaded and installed Descent. It installed successfully and has continued to load ever since.
To sum up: In every case in which I tried to download and install the Descent DLC in my initial installation with everything else, the game broke. I was able to succeed twice when Descent wasn't installed. After playing the game for a while I installed Descent and the installation took.
Again, this might all be luck and magic, but in my tests Descent was a common factor in the game not launching, when I downloaded it with everything else. Also, I suspect it's a very good idea not to let the game launch at all while it's downloading and installing anything--even though the game will prompt you as to whether you want to launch it.
That was my magical solution. I hope it works for someone else.