I haven't read your book as such, but I have some general comments:
There is a popular idea nowadays to make YHWH another sun god. Thing is, the oldest parts of the Bible like the Song of Deborah, have more storm characteristics - which also fit in more with Canaanite El and why Baal would then be placed in opposition or in attempted syncretisation with YHWH under Ahab. Solar imagery is common in the Bible, but this is more when speaking in light of a Montheistic or at least Monolatric way - as the Sun is a good metaphor for a monotheistic God, like the Aten in Egypt or the late Roman Sol Invictus.
Joshua's name clearly references YHWH, so either a solar characteristic references the conception of a montheistic YHWH, or this solar association is more likely secondary to this miracle account, and not a primary one.
Besides, Joshua isn't much of a solar figure outside this one event and a dubious etymology for Timnath-Heres. This is different from say Samson; whose name invokes the Sun, is opposed to the marine fertility god Dagon, has long hair like rays of the sun, is destroyed by Delilah which can be read as meaning night; he is active around Beth-Shemesh, meaning House of the Sun; etc. So it seems a bit of a stretch here, especially as there is a much better candidate for solar demigod in Israelite lore.
As to poetic doubling, poetic antitheses like Sun and Moon are also common.
Reading it as refering to a solar eclipse is quite common, there is even a fair canditate in 1207 BC. I don't know, this is one of those strange passages. As far as I am aware, the Samaritan book of Joshua says nothing at all about this event of the Sun and Moon standing still, so if anything, we aren't necessarily dealing with an 'old half-supressed solar tradition' rather than a purely Jewish narrative. After all, it is not found in common with the Samaritans, who share much of the rest of the Judges narrative and much of Kings.