I'm specifically looking for sources discussing the Battle of New Carthage. I've been looking for other primary sources but I've found none. Even the bibliographies of all the secondary sources I've looked at have nothing relevant. So, am I missing something, or are those two really it?
Unfortunately, there's not a lot left earlier than Polybius. Much of the work historians of Ancient Rome do is try to figure out how the surviving sources (often written centuries later, as Livy in this case) got the information they claimed to have.
Romans started writing history right around P2, and the first Latin history was Cato's, and Cato had fought in that war. Not at New Carthage though. But you can put a historian within living memory of that battle.
Polybius himself had connections with the Scipiones: he was the tutor of Scipio Africanus' adopted grandson and he would have had the family traditions to work with. It's interesting that Polybius and Livy have different accounts (it's been a long time since I compared them, but I remember the geography being different), and that suggests they had different source material.
There may be fragments of older historians like Cato that mention Africanus, but I don't know them, and they aren't referenced in Brill's New Pauly. I don't have access to Pauly-Wissona or Broughton, but those will have the best lists of the evidence.
Here is the New Pauly bibliography for Carthago Nova and Scipio Africanus:
S. Ramallo Asensio, La ciudad romana de C. Nova, 1989
A. González Blanco, La historia del Sud-Este peninsular entre lo siglos III-VIII d. C., in: Antigüedad y Cristianismo 3, 1985, 53-80
M. Koch, Die röm. Gesellschaft von C. Nova nach den epigraphischen Quellen, in: F. Heidermanns, H. Rix, E. Seebold (ed.), Sprachen und Schriften des ant. Mittelmeerraumes, 1993, 191-242
Tovar 3, 190-197.
H. H. Scullard, Scipio Africanus, 1970
Id., Roman Politics 220-150 B.C., 21973, 290-303 (trials).
I think Scullard's going to be the best bet.