Have you tried using Joy2Key and just bypassing the built in gamepad support by emulating a keyboard? I know it's not ideal but for a game like this I think it would work pretty well.
My XBox-One controller worked right away. I haven't used ds4 in years though it seems like I would sometimes run into issues with it. And I used to just use Joy2Key as a backup solution. It's freely available -> https://joytokey.net/en/
Good luck! This game is definitely worth the extra effort to get it going.