I have this same exact setup. I do not use the Ability Menu button--my abilities are bound to the Cross-Pad because the Swipe Pad is, and always has been since I started playing back in 2014, completely unreliable in terms of being able to accurately and consistently activate a specific ability at any given time... not to mention, since the introduction of abilities with "press-and-hold" functionality such as Ivara's Quiver, Vauban's Minelayer, Wisp's Reservoirs, etc, trying to use the Swipe Pad with those types of abilities is about as effective as trying to bite your own ear (how does one, exactly, press-and-hold a swipe?)
I might CONSIDER mapping the Ability Menu button somewhere in my controller setup *IF* DE would make it so that, when configuring the button settings for the Ability Menu, you could assign abilities to the Cross-Pad directions--as it stands now, you can ONLY map abilities in the Ability Menu to the Triangle, Square, Circle and X buttons! And the Cross-Pad? Well, the ONLY thing you're allowed to assign to any of the 4 Cross-Pad directions is either:
(1) Focus and Transference, or (2) Tactical Menu. THAT'S IT. WHY SO LIMITING, DE??????
I'm sorry, but I do not find this "solution" to be anything to cheer about.
I have been playing this game since the launch of the PS4, and I have the controller configured in a way that works reliably for me (which is not much different than the ORIGINAL default controller setup). So having to move my Melee Attack button to somewhere other than R1 because DE insists that I throw six years of muscle-memory to the wind and utilize (read: be hobbled and limited by) their new "flavor of the month" controller setup just to be able to do what I ALREADY USED TO BE ABLE TO DO before they screwed around with the controller setup (AGAIN!) ... no. This is NOT acceptable.
There is an old adage about fixing things that aren't broken that comes to mind here. As Angry Joe so succinctly puts it... YOU DONE F'D IT UP!