I would kill for a button combination on ps4 to take screenshots >.> I have to press the Share button, which opens a PS4 menu (fully blocking my game) and press triangle to have it save a screenshot.. and then wait a few seconds for it to load before it brings me back to my game -.-
That aside, I doubt they will actually implement a fix for this, as I dont think they view this as a priority (meaning I dont think enough people have complained about it for it to show up on their radar..
If you cant disable it using the keybinds, your only option may be to just.. get in the habit of waiting a bit after you autorun.. press L1, wait one second, then open your menu. After a little bit it'll become habit and you wont be taking all the accidental screenshots. Not sure what else you can do though..