Cabinets with existing dowels in the wrong place. How do I fill for new hinges?
To try to plug that for the sake of getting better grip for the screws, will not be worth it.

Others may not agree but I would not hesitate to use a self-centering bit like a Vix bit and drill the new pilot hole where the hinge dictates- right at the area where the plastic and wood meet. The wood will be hard enough to hold the screw, and what little grabs the plastic insert will add a little more hold, and compress the plastic in tighter.