You've sorta answered your own question -- with some qualifiers.Based on conventional associations the planet 'ruler' or principle behind the sign over the Ascendant (of an accurately cast chart) is considered the chart ruler. However, that is a sign-based association. Planets and their aspects are stronger. So if there is actually a planet conjunct and/or parallel the Asc it may be stronger or more influential. But it still does not override the planetary principle of the sign over the Asc, but is unavoidable in interpretation.
James Woods has Leo rising, so the Sun is considered conventionally speaking to be the 'chart ruler.' However, Saturn is conjunct his Asc and is evident in his appearance and ambition. Which is the chart ruler? Does it matter, or is answering the question an attempt at reductionism? We need to let astrology remain complex instead of trying to simplify it for our convenience.
My dad has Cancer rising with Saturn closely conjunct the Asc. Conventionally, he is supposed to be Leo rising because of the time of birth he was given, but I can assure you not only is there nothing in his personality that is Leo at all, there is no hint of Solar/fire at all. I had to rectify his chart and he is unquestionably Cancer rising as evidenced by his one word answer to my question of how he would sum himself up. After thinking for a moment he said, "Inuitive." Plus, he is a quiet, reticent, family man. No one in our family would describe him in a way that matches up with astrological Leo rising personality. So in the rectification procedure it became very obvious that Cancer rising conjunct Saturn works very well and was proved out as well as can be done. So the Moon is his chart ruler, but Saturn is so close to the Asc of his correct chart that it is very evident in his personality and life and unavoidable in the interpretation of his chart. Which is stronger Moon or Saturn? That can only be answered by looking at the total condition of his Moon in Virgo, etc. Ultimately, it doesn't matter. Saturn, the actual planet, is there at his Asc. Moon is only implied through Cancer rising, yet is still evident in his answer, "Intuitive." What complicates matters is that both Uranus and Pluto are parallel his Asc, but there is no question he is a Saturnine, work-oriented person of principle, well organized, firm not emotional in his dealings, and very parental. Classic Saturn (for a Cancer rising personality).
Astrology does not benefit from reductionisms for convenience or ease of learning. We inevitably end up un-learning some things in order to learn more.
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"Drift like a cloud and flow like water, seeing that all life is a magnificent illusion, a playing of energy, and there is absolutely nothing fundamentally to be afraid of." -- Alan Watts
Soul Stars Astrology by The Declinations Guy
Expert Rectification