Hours and Hours of research and experimentation later and I believe I have a more complete knowledge of controllers, their drivers, and this problem. It isn't exclusive to 9 Parchments. Other games, like Dark Souls 2, suffer from the sporadic right stick, the mismatched buttons, and the constant input errors. It appears it has something to do with X-input vs. Direct Input, but it goes deeper than that.

When you use the DS4Windows software you are plugging in a PS4 controller and it is using a virtual bus to disguise it as an XBox controller. According to windows you have both controllers plugged in. Some games are fine with that because they don't accept direct input, only X, but games like the above mentioned, and 9 Parchments, may accept both. And, they may accept it at the same time. Suddenly you are feeding all sorts of input into the game, and it goes completely crazy.

DS4 has a built-in solution to this, but it is somewhat difficult to get working in more recent Windows, especially if you have Steam, Nvidia, and Xbox software on your computer. This mode is called Exclusive Mode ("Hide DS4 Controller" in the settings). It hides the port the normal DS4 controller shows up on, making the simulated Xbox controller the ONLY controller your computer can see. It's great.

But, Exclusive Mode will probably come up with red fail text in the bottom of the DS4 box the first time you click on it. This is because many game services (Steam, Nvidia Experience, Xbox, U-play, Origin, and whatever else) want your controller to reference them. They want that middle playstation button to summon their overlay, and so they grab onto the driver and won't let it go. In this case, they are grabbing the wrong driver. The one for the PS4 controller. Now when DS4Windows tries to go Exclusive the driver is being used, and it can't isolate it.

So, you need to close down all overlay services when you start it up. Shut down Steam, turn off Nvidia Overlay, take out Xbox for Windows Overlay, and anything else you have that wants to run over your game and use that lovely controller button (GOG Galaxy doesn't seem to reference the driver at this point, so I never had to close it).

Once all of your other services are closed you can open DS4Windows, Press "Hide DS4 Controller," and bam.

9 Parchments works like a charm with Xbox output from your PS4 controller. So does Dark Souls 2, for that matter.

Or, like I mentioned in my previous post, you can just turn off the DS4Windows software and play with its native PS4 Controller support, which is lovely. But, if you like custom lightbars, a mouse touchpad on the controller, and Xbox game support, this method is for you.