The only house system you should be using is Placidus and not one made-up system we know nothing about and that has a name related to the king of the Gigantes, and thus representative of the chaotic, destructive aspect of nature.
I write respectfully and kindly in addressing your post, to explore the topic further.
Quote from Mageson:
"
The Neoplatonist philosopher Porphyry stated the celebrations that with done on the festival of Saturnalia where about the "freeing of souls into immortality". This is done by the Magnum Opus. Saturnalia is based on Liberation and dissolution of the Magnum Opus its based on the sun entering Capricorn:"
HP Mageson writes about Porphyry here too: https://www.ancient-forums.com/viewtopic.php?f=24&t=21151
HP Zevios mentions him briefly here: https://www.ancient-forums.com/viewtopic.php?f=24&t=3103
Porphyry (name meaning "purple clad") is very well known neoplatonist philosopher. His teacher was Plotinus, one of the most influential Hellenistic philosophers of his time. Chances are if it was a topic in the ancient world, he already had writings on it. He was also a hardcore pagan and wrote a series of works against christianity (which were banned by the church).
The name we all know him by (Porphyry) came from one of his teachers, Cassius Longinus of Athens, because it's most likely a reference to purple dyes due to his Phoenician heritage. Porphyry was a common name in Tyre, where he came from (the city of purple). This is one of the city's well known exports, which is both rare and difficult to produce. His given name was name "Malchus" which meant king in semitic languages. (we'll leave that name Malchus up for debate, due to his Phoenician heritage).
You can read more about Porphyry here.
https://plato.stanford.edu/entries/porphyry/
His house system is finding the quadrants of the chart, and dividing it by three equal parts. It's one of the oldest system of a quadrant house division. If we have no astro.com, then it would probably be easier to calculate by hand. They worked with what they have.
As for the ancient Giant (from theoi):
Porphyrion could mean "Surging" from the Greek word porphyreôs, a term applied to both the surge of battle and the sea; or "Gleaming Darkly" from the word porphyrô; or else "Purple-Coot" from porphyriôn. Also "purple one."
There may be a relation, but the meaning is just the color purple.