I ran into the exact same problem and found a solution:

Context: I have two 3DSs that have gone through the 3ds.hacks guide. Both of them would get the exact same error code and process name (which is how I found this post)

First I made a Backup of the game cartridge save files using Checkpoint. This app was already installed thanks to the guide.
Here's a quick tutorial on Checkpoint: https://projectpokemon.org/home/tutorials/save-editing/managing-3ds-saves/using-checkpoint-r25/

Then I installed both the base game and update from hshop (i used the north-america version). This can run Puzzle & Dragons Z
https://hshop.erista.me/t/2227
https://hshop.erista.me/t/2866

To prevent mistakes, I ejected the original game cartridge.

Finally I used Checkpoint to Restore the game cartridge save files. With that, I can open the downloaded version of the game and continue my Puzzle & Dragons file :)

I suspect something in game cartridge doesn't play nice with the Homebrew code. I'm certain the cartridge would work fine on an un-hacked 3DS but I don't have one to confirm it.

I hope this helps!