You're very inquisitive lately.
You're right about the ruler of the ninth being Jupiter, but not via an association with Sagittarius.
The comparison of signs to houses is intended for medical astrology, and the comparison is made via the human body and it's ailments, where a system of twenty-four variables gives considerably more scope than twelve. However, the comparison pretty much ends here, but it has been blown out of all proportion.
Chaldean rulerships give us Saturn as the natural ruler of the eighth, not Mars.
If we refer this to the fleeting comparison we might infer between planets and signs, the antique attribution of Saturn to the eighth, makes the Scorpio/Saturn connection with death and not
sex, much clearer. Venus/Leo would be the fifth, as the fifth is the rulership and joy of Venus.
I wouldn't make too much of a meal however, of correlating the signs with the houses, Leo is a barren sign, the fifth the house of fertility!
However, in medical astrology, Leo is the heart, and the fifth is too (house of love), but such correlations start and end in the medical sphere.
This what I mean about such a tight, stringent correlation of house = sign = planet, which has got out of hand.
Considering mutual reception by house and not by sign would not be conventional horary practice, however, it's an interesting idea, so why not give it a try.
For the record, the traditional rulers of the houses, and their 'joys' in brackets (or parentheses).
1 - Saturn (Mercury).
2 - Jupiter.
3 - Mars (Moon).
4 - Sun.
5 - Venus (Venus).
6 - Mercury (Mars).
7 - Moon.
8 - Saturn.
9 - Jupiter (Sun).
10 - Mars.
11 - Sun (Jupiter).
12 - Venus (Saturn).
To put it another way:
Saturn - 1 & 8 (12)
Jupiter - 2 & 9 (11)
Mars - 3 & 10 (6)
Sun - 4 & 11 (9)
Venus - 5 & 12 (5)
Mercury - 6 (1)
Moon - 7 (3)
It pays dividends to give this system some serious contemplation, have a think about it, it'll enlighten you. Placing this set of rulerships in a circular arrangement, is more of an eye-opener.