The only way to achieve what you desire is to refinish the floor. The only way to do this is to sand the entire floor with heavy, professional equipment, taking off a measurable thickness of wood in addition to the finish. This is a "wood" floor and this is really what is so great about wood, that it is very forgiving. If this were a vinyl floor you couldn't refinsh it. Save up and do it right. If you still don't want to refinish the floor in the normal manner then you need to buy a rug to cover the lighter spot.