Joshua, the amelekites and history

At 1 Kings 6:1 we are told that 480 years had passed between the Exodus and the fourth year of King Solomon. The date is schematic [twelve generations of forty years], and, as we have seen, it balances the Israelites' length of time in Egypt [430 years at Exodus 12:40]. If we took it literally, it would put the exploits of Joshua back at c1420-1400 BC: it is not, however, a correct figure.
Robin Lane Fox, The unauthorized version: truth and fiction in the Bible

I'm trying to get my head around ancient history, starting with events described in the Old Testament, but probably mythical. That's to say, the bloody events described mainly in the book of Joshua. In the Hebrew Bible [he's a much more minor figure in the Torah] Joshua became the leader of the Israelites after Moses. Bible chronology isn't entirely reliable, as my quote indicates, but scholars are more or less agreed that he flourished between 1450 and 1370 BCE. That's to say, that's the period in which he's calculated to have lived, had he lived at all.

The Joshua of the Bible is an almost monotonously victorious general. His first victory was over the Amelekites – the first of many slaughterings of a people destined to become the archetypical enemy of the Jews. Next he crossed the Jordan, with Yahweh parting the waters as before at the Red Sea, and was bloodily victorious in battle against Jericho, Ai [after a brief glitch, see Joshua 7: 3-26], Gibeon, Makkedah, Libnah, Lachish, Gezer, Eglon, Hebron, and Debir. Chapter 10 of Joshua ends on a high note:

So Joshua smote all the country of the hills, and of the south, and of the vale, and of the springs, and all their kings: he left none remaining, but utterly destroyed all that breathed, as the LORD God of Israel commanded. And Joshua smote them from Kadeshbarnea even unto Gaza, and all the country of Goshen, even unto Gibeon. And all these kings and their land did Joshua take at one time, because the LORD God of Israel fought for Israel.

To most modern consciences, this is sickening stuff, and the fact that we have not a shred of external evidence that this Yahweh-sanctioned splattering spree ever took place, or that Joshua or Moses ever existed, hardly makes it more palatable. But if we put our feelings aside, what evidence do we have, either from archaeology, or from external records, of these Biblical places and peoples and their histories? For it should always be emphasised that the Bible is by no means a history book, and every supposedly historical statement found therein should be treated with the utmost scepticism.

The only extra-Biblical reference I've found regarding the Amalekites so far comes from one Nachmanides, a mystical Jewish scholar of the thirteenth century, whose own gleanings would have come from the sacred texts. This isn't to say that the Amalekites were purely fictional – it's very likely that they were an aboriginal group in southern Canaan or Palestine – but the name should give us pause. The Amalekites are named for Amalek, mentioned in two genealogies [Genesis 36:12 and 1 Chronicles 1:36] as a grandson of Esau, Jacob's brother. Jacob and Esau, though, are as mythical as Adam, so at this point I've reached a dead end so far as the Amalekites are concerned.

We can say more that's extra-biblical about some of the other places I've mentioned. A lot of archaeological work has been done at the site of Jericho, unearthing more than twenty successive settlements going back 11,000 years. The results have proved extremely problematic for the Bible-is-history pundits, because unfortunately the author of Joshua provided details of the battle which are subject to empirical testing