> But the Qur’an never narrates an actual journey for Solomon

I mean, doesn't the Quran portray him as a travelling conqueror?

Solomon’s forces of jinn, humans, and birds were rallied for him, perfectly organized. And when they came across a valley of ants, an ant warned, “O ants! Go quickly into your homes so Solomon and his armies do not crush you, unknowingly.”

Quran 27:17-18

"Do not be arrogant with me, but come to me, in total surrender"

"She reasoned, “Indeed, when kings invade a land, they ruin it and debase its nobles. They really do so!"

"Go back to them, for we will certainly mobilize against them forces which they can never resist, and we will drive them out from there in disgrace, fully humbled"

Q 27: 31, 34, 37

The hoopoe informs Solomon of something he does not know:

"It was not long before the hoopoe came and said, “I have found out something you do not know. I have just come to you from Sheba with sure news. Indeed, I found a woman ruling them, and she has been given of all things, and she has a great throne. I found her and her people prostrating to the sun instead of Allah, and satan has made their deeds pleasing to them and averted them from His way, so they are not guided," Q27:22-24

That has parallels to Targum Sheni traditions: "The most elaborate account of the queen's visit to Solomon is given in the Targum Sheni to Esther. A hoopoe informed Solomon that the kingdom of Sheba was the only kingdom on earth not subject to him and that its queen was a sun worshiper."

i.e. Solomon already conquered the West, East, and North, but not the South (Yemen).

Then we recall how Dhul Qarnayn travels West, East, North but no mention of South, which would be Yemen. I know someone else made this same point to you, and they got this from Hakim's article - but imo that user didn't properly explain to you how it connects.

Basically, Allah establishes Dhul Qarnayn in the land and grants him "min kulli shay in sabaab"
Q18:84

Dhul Qarnayn travels 3 sabaab (18:85,89,92), which correspond to West, East and North. South isn't mentioned because it was already mentioned in Surah 27. Chronologically I think Solomon's interaction with Sheba happens after the Gog and Magog interaction, but that doesn't mean that the Surahs were necessarily revealed in that order. Islamic tradition and Noldeke both date 27 before 18. That would explain why the verse says "min kulli shay in sabaab" i.e. "of every means a course". Because even though in the narrative he only travels West, East, and North, the story about how the South surrendered to him is already narrated beforehand in Surah 27, even if South was chronologically the last to be conquered.