Please Help! (787 + LNAV = DEATH)

If it’s a double binding issue I would suggest to remove all bindings and start from sratch.
It’s possible that your keyboard, mouse and joystick assignments are conflicting with each other and when you are e.g. turning your head, or the camera, your 787 starts banking.

If it’s a deadzone issue I would initially increase the deadzone to 25% and if the problem doesn’t reoccur, try reducing it to 20%, etc. etc.