You are not going to get your miracle. Screening and recoating is standard maintenance. Do one room at a time so the furniture can move to the adjacent room to clear the floor.

If your floor is still in pretty good shape with no wear-through to bare wood, then you can do what you want with a buff and coat.

Different finish manufacturers have different systems to do what you want here. For example, Bona's system uses a moroon buffing pad and their Prep chemical cleaning agent. Basic Coatings uses a system that uses their Tykote cleaning agent.