Can't play FH4 using a wheel and a controller simultaneously- help

I have a Logitech g29 racing wheel, and I use a Dualshock 4 as an E-brake.
In FH4’s settings, I use two binding profiles- one is for the wheel and the other is for the controller.
When I try to play this way, whenever I touch the controller, the game disables all the inputs from the wheel and pedals for a few seconds, making the game unplayable.
(On most Dirt games I can drive perfectly fine using this method).

I tried using Forza Emuwheel. This allowed me to bound both the wheel buttons and the UpRight joystick button on the controller to the same wheel profile.
But for some reason this didn’t work and I got the same result. I guess Forza still recognizes that I use a controller (even though the button is mapped to a wheel profile), and switches to the default controller profile (which I don’t think I can delete).

Any idea on how to solve this? Any suggestion will be much appreciated.

Maybe this?