We hate to be the bearers of bad news, but this is without a doubt is one situation when you can't make use of existing materials. It would not be realistic to expect to remove the majority of the tile without damaging most of it. As patient and careful as you may be, it is virtually impossible to separate the tile from the substrate. Even if you are able to extract a tile intact with out damaging it, chances are that the back surface will not be acceptable for future reinstallation because of the mastic adhesive that remains. Attempts to clean the rear surface of previously installed tile rarely are successful. Part of what makes a tile job a success is working with clean, dry and smooth surfaces.
We are as cost-conscious as the next guy, but believe this would be an appropriate time to purchase new tile for the area. You may wish to consider this a prime opportunity to select something fresh and exciting. The total cost of the tile for the area should be somewhere between $150 and $200. In retrospect, this may not be such bad news after all.