I think there're good points in that article!
GEMINI RISING OF USA AM time CHART
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Let me point out why I think the USA chart is the Sag rising, the more accepted date of July 4. The SOL SIGN is the 60th harmonic sun. This being an 'essential', it is the nature of the nation, and person, the inner self as it were. The USA SOL SIGN of JULY 4 5PM is 19 Gemini. This would be conjunct the STAR CAPELLA, and marks it very much of Gemini quality. The brightest star of the north sky. I think this sign which changes every 12 hours, signifies why the Gemini rising chart gets so many nods, just as you said above.
There is also the USA sun conjunct Sirius on July 4 date. Now I am more than convinced of this, but let me say I do have a Bias. I am a 17 gemini sol degree, and my family name is ADAMS. I believe we are related to the presidents, and am sure of relation to the first governors of massachusetts. Also 77 degrees (17 gemini degree) is Washington DC longitude. My mother was born July 11, same day as John Quincy Adams, and my father oct 28, same day as John Adams. None is just coincidental. By the way, I have Uranus at 13 cancer in the 11th house conjunct the USA sun degree. Hence, The American Sol Astrologer monacre (spelling?).
There are numerous other configurations to the sun and sol degrees to make the SOL METHOD very interesting. One is Thomas Jefferson, a sol Capricorn (like mao tse tung, and Napolean - we were for jefferson, against the others) conjunct the USA pluto. I would also like to point out the american eagle group, for fun. These are sun in late capricorn, including Betty White, kevin costner, Dolly Parton, many others. The Americans like the conjunct to the Eagle star, 0 Aquarius. My wife is SOL 3 Degrees aquarius andmy moon is 14 degree sol aquarius, in the sign of the USA moon as well.
If we progress the USA sol of 19 gemini, we may find the conjunction progressed to the venus, jupiter, and the USA Sun, 14 years after 1776 (1788- Constitutional Venus, 1791 Jupiter, and then 1798/9 leading to the Sun conjunct, which is also square our Saturn. Perhaps the degrees are off a year or so by a degree or less, but the actual rectified birth time could be altered slightly from earlier than 5pm or 5:10pm. But nonetheless, this is all very engaging.
USA sol arc progressions - Gemini 1776-1787, Cancer 1787-1817, Leo 1817-1847 (includes node in early leo conjunction to monroe doctrine (1823) - we take ownership of the continent. The virgo cycle is 1847 to 1877 with Neptune conjunction of 1868/9 during reconstruction after civil war) and the important amendments of that time period. Inventions were manifesting greatly. Libra is 1877-1907 as social immigration and victorian age as well as wild west (libra = california. scorpio 1907-1937, first world war, wealth and depression. sagittarius 1937-1967 proclaims world expansion, new freedom, mashall plan, the rising at 12 sag is 1949, baby boom. Many people. Capricorn 1967-1997 with Pluto 1991 (war in kuwait), selling weapons and Afganisthan vs. Russia, Aquarius 1997-2027 Aquarian technology and internet, conjunct USA Moon is ahead around 2024. Could this mean American becomes the first universal nation on Earth? A country without borders? or something like that.
We must remember USA is in other Pisces (solar progression) and scorpio cycles currently, very watery, concern emotions and human populations. A number of concurrent cycles going on, such as usa constitution, and the world transit cycle of course.