I did a bunch of testing of programs to fix this for me over the last few days (using an Xbox One controller). The 2 I found that worked for me (with 7th Heaven Launcher) were Padstarr and Pinnacle Game Profiler (PGP). I prefer Padstarr right now as it seems more modernized. I think you have to pay for them, but they do come with trials (the PGP trial ran out for me and it is basically useless after that point unless you buy it). For now, I don't see anywhere listing a trial/how long it lasts in Padstarr, but we shall see.
Anyway, with Padstarr, I had to set it to make the game not recognize my controller as a controller, so that the D-pad would work properly based off of the keyboard commands. Everything on the controller works with the profile I downloaded for it too (using morpheus2n's FFVII controller profile with some edits such as making the analog stick make your character run if you push it over 85% in a direction).
I could not get my PS4 controller to be recognized by DS4Windows for some reason, and a lot of the basic controller to keyboard mapping programs didn't work for me, because the game would recognize the controller and would only accept it's inputs as a controller, so that's why Padstarr worked for me as it lets you disable that.