Large Hole Cover Up Ideas

Hello All, I am replacing my old doorbell, and like many others, the doorbell hole is too large to drill/screw the four points when installing the Ring doorbell. I have a solar charger so that is actually big enough to cover the hole, but I ran into the same issue where the four-hole points to drill/screw fall within the existing hole. I thought about just getting a blank cover plate but I am not happy with the look of a cover plate and the new Ring system within the same area. I don't want a bunched up/crowded look. I am looking for a clean solution where I can possibly cover up the existing hole with the new Ring system on top of it, in the same place. Is this possible? Any suggestions?