• Opinion #1 Each row had 6 rings from east to west. There were 4 rows in total and the space between the row centers would be 8 amos. This would put the second row of rings 16 amos (8 + 8 = 16) away from the northern edge of the Altar.
• Opinion #2 Each row had 4 rings from east to west. There were 6 rows in total and the space between the row centers would be 4.8 amos. This would put the second row of rings 12.8 amos (8 + 4.8 = 12.8) away from the northern edge of the Altar.
There does not seem to be any indication in the sources that the orientation of the rows would make any practical difference. If, however, it can be shown that one of these orientations fails to have the second row of rings in full sunlight during the shortest days of winter then this orientation may be ruled out.
Once the height of the Courtyard walls have been set at 40 amos, the shadow cast by the Altar becomes the most influential factor. The closer the second row of rings is to the Altar, the more likely it is to fall within that shadow, and it is therefore Opinion #2 which stands to be eliminated. Well, upon closer inspection I see that Opinion #2 is the one I used in my original sun study and the second row of rings was clearly in direct sunlight. So it emerges that both opinions meet the criterion and neither can be eliminated on the basis of the Altar's shadow.
The other question is the north-to-south placement of the Altar within the Courtyard. Although the dimensions of the Courtyard are given in the Mishnah, some details are omitted, and one of those details is how far the Altar was from the southern Courtyard wall. Various opinions are given among the commentators, but the shortest distance on record is that of the Tanna, R' Eliezer ben Yaakov, who maintains that the Altar was only 5.5 amos from the southern wall. If it can be shown that when the Altar is this close to the south, the shadow of the southern wall falls upon the second row of rings then this opinion may be ruled out. Here is another sun study animation with the Altar placed according to the opinion of R' Eliezer ben Yaakov:
As it turns out, the shadow of the southern wall does not approach the rings at all, and thus we must conclude that the sun study cannot shed any light upon the issue of where the Altar was placed.
SUMMARY The sun study of the Temple walls does not help determine the orientation of the 24 rings north of the Altar nor does it help determine the north-south placement of the Altar.