PFA The three heading method has been around since the 1930s, GPS is just a relatively new slant on it. The original reference is:-
F L Thompson (Langley Memorial Laboratory, NACA), The measurement of air speed of airplanes, NACA Technical Note No. 616, October 1937 Which you can download from the NACA reports server if you hunt around a bit.
Also worth looking at the download section of NTPS' website at
http://www.ntps.edu/Files/ which has an explanation and a reduction spreadsheet (Looks like Doug Gray's paper is very similar). The basic maths is just trig, which is easy enough to derive if you enjoy that sort of thing (personally I think it's a pain and best avoided). I can see why you like his approach however, since it uses GPS track (rather than compass heading, which will contain errors).
Don't forget that you also need the relationship between TAS and CAS, which is the square root of sigma, the relative air density. There's quite a nice free reduction sheet for this online at
http://www.bmaa.org/techinfo.asp (form 043).
If you want a really thorough proof, there's a book called "Performance of Light Aircraft" by an American Boffin called John Lowry - ISBN 1-56347-330-5 which covers it very well. Having said that, he's a little overfond of maths for my taste - as evidenced by his book being the only I've ever read which includes a correction for the distance between the static port and the tyres, which personally I think is going a little far.
Dave I occasionally have trouble justifying the method with some of the more old-fashioned regulators over here. You wouldn't have a graph or two of GPS PEC .v. static bomb shoing your accuracy values that I can steal from you? Oh yes, and welcome to the Flight Test Forum, glad to have somebody of your experience around.
G