I don’t think you’ll need all those loop-cuts there.
Since that door is not going to deform, you can comfortably go with a big n-gon for it and take a similar approach to some elements in the “Press Start” course. So basically place your oval shape where you want it and extrude it inwards, bevel and all. Then connect the oval shape with the rest of the door with a couple of bigger faces. Maybe outset the outer edge of the oval to be able to bevel it too.
If all your fronts are the same, you could then simply copy the door around and resize as needed.
