Not sure if it's something you'd like, but I use this controller and I really love it:

https://www.amazon.com/New-Improved-D-Pad-PlayStation4-PlayStation3-PlayStation/dp/B01HT2TUBQ/

You can set the analog stick to act as the right stick, which effectively deactivates it for fighting games. I use the stick myself, but I find the d pad to be quite high quality as well. As for the buttons, they are very slightly placed differently than the regular ps4 controller, and slightly wider. Their positions are closer to the traditional fight stick layout, but the placement of the x, o, triangle and square buttons still feel easy enough to use with the muscle memory from a regular controller.

Also, don't be turned away because the maker is Mad Catz; I believe another company actually took over the product, and the controller is perfectly sturdy anyway.

One of my favorite features is the ability to set the left trigger buttons to L3 and R3, and the right triggers to L1 and L2. This removes the redundancy of the R1 and R2 face buttons, and gives you two extra triggers :D

I suggest buying a version of this controller that is listed as having the "new and improved d pad" (I linked this one). The older version of the controller, when Mad Catz made it on their own, had a simple + shaped d pad, not the circle one pictured. Just to let you know, in case you find the older one elsewhere. Also, when I bought mine, the controller had a slightly nicer d pad than the one in the picture. :P

Best of luck finding something that works for you! :)