How do you move a 650lbs Rack on Hardwood...

I would use 2ea Hand Carts with phneumatic tires. Place lip of each cart at each end of rack. Place thin piece of something on bottom of rack to prevent the cart's lifting lip from scratching anything. Use the lever action of the carts to lift high enough and roll it on over to where you way it. Have a 3rd person steady the rack.

If the floor is smooth and level, just a steel plate on the bottom of the rack with a single 3/8" hole in the middle attached to compressed air source. Assuming the footprint of the rack is 21" x 24" = 504 sq.in. Divide 650 lbs by 504 sq.in. = 1.3 lbs/sq.in. not that big a deal really.

Get those plastic tracks that refrigerators are moved on. You lay them on the floor and the fridge rolls/slides on them. Like the furniture gliders, only on about 2.5' tracks that are about 4" wide. They interlock too if you need to go further distance. They'd likely be at any home improvement store. If the rack ends up in the closet ontop of them, so what? Ready for removal at some later time.

After reading the various options, I vote for the masonite as the cheapest and safest solution. K.I.S.S.

Others have mentioned it before me.Masonite 1/8 is what you want to use.I've seen it used many times in similar applications or as a floor protector during renovations,remodeling.Just tape it down with red tack tape and roll your rack out on it.
George