The founding fathers simply kept the word "White" ambiguous because they would let the question be settled by democratic vote. And Democracy is what has destroyed the White race, so, ergo, appealing to the founding fathers is in itself a flawed and doomed appeal.
People
have thought about this, and it's been widely written about for hundreds of years. The best scientific racialists in the 18th century all agreed that Whites originated out of the Caucasus region, hence the term, "Caucasian race."
https://en.wikipedia.org/wiki/Caucasian_race (Please ignore Wikipedia's liberal bias; the sources and descriptions of what people thought in the past are still largely true)
To this day, the people of Georgia have their own distinct DNA separate from Europeans, and no one would call Georgians anything but White. For example, Joe Stalin was a Georgian, and to call him anything but White seems ridiculous on its face.
Thus the term Caucasian has a tremendous amount of scientific and empirical support, which holds that Whites originated out of Europe, the Caucasus, and North Africa. Each with their own DNA strands. Now, obviously, European Whites have flourished the most over the centuries due to their highly defensible location, but, it simply isn't true to limit the definition of White to Europe and that's why the term Caucasian has been used for centuries. The term was created by the same Europeans you are espousing.