Jerome Walsh's commentary on I Kings is probably the best thing out there on narrative issues in I Kings. I've heard good reports on it from several commentary reviews, and two people who have used it in their sermon preparation for our current sermon series in Kings have found it very helpful. It's fairly rare that he says anything that evangelicals would find problematic with regard to the nature of scripture, but I did identify one thing when reading his commentary on I Kings 11, and I don't think he can consistently maintain it given other things he says.
When discussing Solomon's failures as a king, Walsh says the following about the narrator's perspective underlying the critical account (from p.136):
Yahweh is described as "the God of Israel" to contrast with the other national deities named in verses 5 and 7. The concept here is very different from our own. The narrator presumes a polytheistic worldview: other gods besides Yahweh existed, and each deity had its own national sphere. The text does not understand Solomon's apostasy as turning away from the only true God to worship false gods. Solomon's evil is that he supported in Israel, Yahweh's own nation, the worship of Yahweh's rivals.
First of all, Walsh uses the wrong term. The view that there are other gods that you shouldn't worship and only one you should worship is not polytheism, which is the worship of many gods. It's called henotheism. There's evidence within the Bible itself that some people in ancient Israel were henotheists. There's actually more evidence that many were polytheists, including Solomon himself according to this passage. But the consistent message of the biblical narrators and prophets is not of henotheism but monotheism. The book of Kings is actually a pretty clear case of this. Solomon's speeches and prayers at the temple dedication are pretty clear that there is just one God who is sovereign over all the earth.
In fact, even four pages later Walsh seems to recognize this. In his discussion of the rebellions Solomon faced from two subjugated peoples (Edom and Aram) and one internal rebellion (Jeroboam), he emphasizes the narrator's theological perspective of Yahweh's sovereignty over the doings of those in other nations (p.140):
The effect of this heaping up of parallels is to recall that both Moses' and David's careers were divinely directed, and thereby to intensify considerably the impact of the claim that "God raised up" Hadad and Rezon. The same Yahweh who raised up Moses as Israel's savior, the same God who raised up David to be Israel's ideal king, now raises up adversaries to oppose Solomon. The punishment of Solomon and the impending disintegration of his empire become part of the sacred history of Yahweh's dealings with Israel, on part in importance with the Exodus and the covenant with David.
Such a view of Yahweh's role with respect to other nations doesn't necessarily require thinking the other gods don't exist. They might just be fairly impotent beings in comparison with Yahweh's sovereign might. But it's hard to see it as consistent with the view that the only reason to worship Yahweh is because he's the god who happens to be Israel's god, whereas other nations have real gods who happen to be their gods. It's very hard to put Walsh's own view of the narrative position of Kings together with his statement that Solomon's sin is disloyalty to the god who happens to be Israel's god. The text itself commands the view that Yahweh is sovereign over other nations in a way that there's no reason to consider worshiping them even if they do exist. In fact, any acknowledgement of their existence is consistent with thinking of them as something like demonic beings whose existence and actions are all subject to divine sovereignty in the same way the human figures in these accounts are.
Now I'm well aware of the view in scholarship that takes some of these accounts to have been written from different theological perspectives. The idea is that earlier materials assume many gods, and later authors added stuff that assumes one sovereign God. Walsh indicates agreement with this elsewhere (e.g. in note 9 on p.112). But Walsh is a narrative commentator, committing to dealing with the final form of the text. Surely if the final compilers agreed with the orthodox view that there is just one sovereign God, they would not have meant the discussion of Solomon's sin to reflect henotheistic concerns but monotheistic concerns. Anyone who could endorse the understanding of Yahweh's sovereignty over foreign kings could not think of those kings as properly worshiping their own gods over Yahweh, since Yahweh is the supreme God. Such a compiler/narrator would therefore not accept the view Walsh attributes to the narrator, and this is true even if many in Israel did hold such a henotheistic view at the time these events are describing. (Since many actually held full-out polytheism, which is what the text is criticizing, it's not a major concession to think many were henotheists as well.)
So I think Walsh's contention is extremely hard to reconcile with what he himself recognizes about the narrator's theology, and that's even conceding for the sake of argument that the original narrator of some passages was a henotheist (which I don't think is true to begin with).