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One thought we had was to do a first coat or two with water and then apply the oil finish later (on the theory that it wouldn't be as orange that way) Or is that crazy?
Yes, it's crazy. The reason your contractor wants to use oil is he, along with many others, think an oil-based polyurethane "feeds" the wood somehow, imparting something extra that waterbased finishes don't. The difference is in the "vehicle" or "carrier". One is a solvent and one is basically water with solvents. Neither will penetrate that much but the oil-based poly appears to because of it's ambering effect. If you want to "feed" the wood, I suggest a tung oil finish like Waterlox.
http://www.waterlox.com/
But that product will really amber the floor. If there is a small out of the way area, consider doing some tests with different finishes on the raw, already sanded wood.