Dear Herbman,
I do not have any significant evidence for my statement, and I probably should not have passed it off as a definitive infallible hypothesis. I certainly ope that it wasn't mistaken as such. What I used to come up to that conclusion was merely logic and critical thinking as you claim in your hypothesis.
Simply because, we know very clearly and we can witness anytime the sun rising from east and setting to the west, it seems more probable that the differing factor is perspective. This is similar to your conclusion however, your hypothetical perspective is not only spatial but also temporal.
Not only that, but it seems you also attempt to make the claim that left and right in Arabic, actually mean North and South.
I do not think my hypothesis is correct, but I genuinely doubt yours is either and this is not to foster confrontation among us, just to improve on our critical thinking and studiousness in Quran.
It is well established through out the text that l-yamini and l-shimali mean right and left.
Look at verse 16:48
16:48
Awa lam yaraw ila ma khalaqa Allahu min shay-in yatafayyao thilaluhu AAani
alyameeni walshama-ili sujjadan lillahi wahum dakhiroona
Have not they seen [towards] what Allah has created from a thing? Incline their shadows to the right and to the left, prostrating to Allah while they (are) humble?
According to YOUR translation this would indicate shadows incline to the south and north. However it does not make sense in physics/optics that an illuminating object traveling westward and facing the Northern direction can cause other objects below itself to cast shadows southward. Go stand outside and place a stick in an open place where the sun light cannot be blocked by buildings or other natural objects. The shadow will never cast southward.
This alone is enough to say that at least l-yamini in this verse does not correspond to south it just cannot. It would be highly illogical and disproving of our ability to successfully observe nature to claim otherwise.
This is but one example, the Quran has many more instances of the usage of the root words ya mim nun and shin mim lam. They simply mean right and left.
I think it is innovative that you attempt to build on the same idea that perspective must be the issue, however, introducing more agents as translation error and duration of event(temporal factor) does not necessarily help us get to a sound conclusion. It rather adds unnecessary complexity (parsimony) and suggests the very ridiculous idea that Arabic is such a complex idiom that the people speaking it do not even know what left and right even is.
There are a few other flaws with your hypothesis. (Again my hypothesis could probably be utterly wrong too, I just want to arrive at a sound conclusion bereft of clear inconsistencies).
1)You say that left and right alone is meaningless but there is a clear reference in the verses which is the cave with the boys in it and the open space thereof..
2)Because we do have a clear reference point, I think to bring in the idea of the solstices is also not demonstrative of astronomical awareness as solar analemma shows us that from a specific vantage point throughout the "solar year" the sun does not completely change its position to any extreme directionality as north and south. Solar analemma cannot possibly be what we are being described in this verse as analemma is visualized by taking pictures of a celestial body from the same geographical location and at the same time each day for a year or whatever desired duration. This conflicts with what the verse describes because we clearly have a rising and setting. As seen emboldened in Surah18 Aya 17 below.
3)In the Verse we see a clear description of a sun rising and sun setting. This is what you are neglecting in your hypothesis. At this point realizing that the description is of a sunrise and sunset left and right become trivial and meaningless. All that needs to be adjusted is perspective. However the right perspective is paradigm-shifting.
I have made some highly simplistic diagrams to allow a better visualization of my hypothesis.

"and when it set, passing away from them to the left while they (lay) in the open space thereof"To remind everyone of the verses
18:17
Watara alshshamsa itha
talaAAat tazawaru AAan kahfihim thata alyameeni wa-itha
gharabat taqriduhum thata alshshimali wahum fee fajwatin minhu thalika min ayati Allahi man yahdi Allahu fahuwa almuhtadi waman yudlil falan tajida lahu waliyyan murshidan
And you (might) have seen the sun, when it rose, inclining away from their cave to the right, and when it set, passing away from them to the left while they (lay) in the open space thereof. That (was) from (the) Signs (of) Allah. Whoever Allah guides and he (is) the guided one, and whoever He lets go astray then never you will find for him a protector, a guide.
18:18
Watahsabuhum ayqathan wahum ruqoodun wanuqallibuhum thata alyameeni wathata alshshimali wakalbuhum basitun thiraAAayhi bialwaseedi lawi ittalaAAta AAalayhim lawallayta minhum firaran walamuli/ta minhum ruAAban
And you (would) think them awake while they (were) asleep. And We turned them to the right and to the left, while their dog stretched his two forelegs at the entrance. If you had looked at them, you (would) have surely turned back from them (in) flight and surely you would have been filled by them (with) terror.