Hi Iam in the same situation. I want to use my 12.9 Ipad Pro as remote play device for the Playstation. For this i have the app "playMira". It works flawlessly.
i also bought the steel series stratus xl controller. But in comparison to the original ps4 controller i must say, that you feel that this stratus is not the same as the original (no r3 and l3 buttons!) ... I hope that i get used to it after time