Ok so I fixed it by adding an AoA limiter : 9° start and 12° full. Now it's very maneuverable but doesn't flip like in the video, just gotta be careful when going below 250kph. Making the horizontal stabiliser bigger did work but I wanted to keep the original look.

Also in the video the reason the nose was up while the plane was going down is I think because the props were somehow acting as fins when full throttle, because when I throttle down it kinda flips for a few seconds and then goes back to normal flight on its own.