Related to this question though much more specific: are there any clues we can glean about the historical situation of the Battle of Ten Kings relative to the Ramayana or other well known events? Maybe through genealogies etc?
Well, the battle of ten kings predates the Ramayana for sure and does take place in this manvantara. But it is not so easy to date it.
We know Ramayana took place in 24th Treta Yuga in this manvatara.
From RV Mandala 7 Hymn 18, we know one of the combatants in Battle of Ten Kings opposite of King Sudas was Puru
- Indra at once with conquering might demolished all their strong places and their seven castles. The goods of Anu's son he gave to Trtsu. May we in sacrifice conquer scorned Pūru.
The aforementioned Puru is son of Yayati. His brother Anu is also mentioned in the verse.
Yayati's father was Nahusha, who was son of Ayu. He in turn was son of Pururavas. His father was Budha and grandfather was Chandra. And Chandra was born along with his brothers Dattatreya and Durvasa to the sage Atri. Now as per Matsya Purana, Dattatreya was born in 1st Treta yug of this Manvantara (Ch 47 verse 242).
So the battle of ten kings has taken place between 1st treta yuga and 24th treta yug. In Ayodha Kanda (Verse 46), Lord Rama makes a reference to Yayati and from it we can make out that that the latter lived much earlier
As sage king named Yayati in olden times left the heaven and reached back heaven again, I shall be back to the city from the forest, after fulfilling my promise