I have a white starfire from 67. I wondered if it was a custom order as it it has quite a chunky neck on it.
Trimbo my memory's not what it used to be, but I recall a thread about a white Starfire from many years ago, and I seem to recall it was ID'd as a factory re-paint for color, but I could be all wrong.
Don't ever recall hearing about being able to special order a neck profile (as opposed to nut width) though.
White Starfires are so unusual that I have to wonder if yours might not be the same one we discussed all those years ago, in any case, I'd bet our guru Hans Moust could tell you, as I think he was the one who ID'd the previous one:
http://www.guitarchives.nl/guitarsgalore/
(PS I love white guitars in general and that one's a
knockout!)