D, there is one important question and that is, how much thickness remains over the top of the tongue of the tongue and groove joint. Flooring loses thickness as it's walked on and more as it's refinished. It only has so much usable life and that's the thickness between the top of the floor and the top of the tongue for the tongue and groove joint. When that gets to be less than 1/8", or will be less after another refinishing, the usable life of that floor is gone. The wood will start cracking from the stresses of people walking on it and this applies even it you relay the floor "upside down" from it's current orientation.
The one thing that you could do is to remove the floor, rip off the tongue and groove sections, remill T&G joint shapes and relay the floor. My feeling is that the cost of tool and equipment, even with your "free" labor would not really make this attractive. You would be faced, at some time in the future, with going through the process again as your floor continues with it's natural wear. And this "new" floor will be starting out with most of it's life already gone.
I'm not saying not to do this. I am suggesting that you take a hard look at what you are doing first, let us know the real situation, and continue with asking the questions starting from a better knowledge base.