Infants asking for bread means they are suffering, not just being killed.
You cannot ignore the fact that God testifies about Himself that His governance takes the form of punishment, but of a general punishment in which even the innocent suffer.
Abraham our forefather also argues, “Will You indeed sweep away the righteous with the wicked?”—which means he thought that would happen if he did not argue with the Master of the Universe: don’t do this.
That is regarding Rabbi Eliyahu’s words.
As for the actual question you mention at the end—what do you really think? How can God be considered moral?

My starting point is that if God acts morally, then such conduct is impossible. After all, these verses, if that is indeed their meaning, contradict “His mercies are upon all His works,” or at least empty it of content (if you insist on defining this itself as His moral conduct). And likewise regarding “visiting the iniquity of the fathers upon the children” and “each man shall be put to death for his own sin.”
If one accepts the fundamental conception that some global event is an act of the Holy One, blessed be He—which in my view is not correct, at least not in our generations. But when there was prophecy, there was someone who could tell us that this was the case, and then it probably was true—even then it still must be that harm to infants (that is, their suffering, not necessarily their death) is out of the question.
Although we have become very used to living with this contradiction, it is a contradiction and therefore unacceptable. So in my view one must do here what the Sages and the commentators do everywhere else: interpret the verses in a way that does not contradict morality, even if that is not according to the plain meaning of the text.
Here are a few possibilities I thought of:
1. Perhaps there is room to say that this is a threat about what is expected, meant to deter and illustrate the magnitude of the impending disaster, and not a description of what actually happened. The Sages attribute Lamentations to Jeremiah (though some wrote that it was his lament after the events).
2. Perhaps this is an exaggeration in a lament text written after the fact in order to sharpen the sense of suffering and disaster.
3. There too one could say that the war and conquest brought suffering upon infants, and the Holy One, blessed be He, simply did not intervene. Alternatively, He stopped protecting the public and thereby enabled the enemy to win. A public that sins disconnects itself from divine providence, and the results are whatever human beings and the forces of nature will do. Still, this requires further examination.

To conclude, because of interpretive problems like these, I generally do not engage in the Hebrew Bible and aggadic literature. It will not change my moral views, and interpretation can at most change my reading of the text. So what is the point of all this, if the conclusions are already known to me from the outset?! Of course, one could say to me: from where you came. Meaning, here is the proof that one can change one’s views through studying the Hebrew Bible. But in my opinion, even among those who disagree with my theological views, no one really changes his moral outlook. I do not think there is any sane person who would advocate collective punishment of infants because of these biblical passages. At most they will say that the Holy One, blessed be He, has His own considerations, and so on. Their moral outlook will not change (unless it was distorted from the outset).

I don’t know what to say about your excuses.
One thing seems to me that they are very strange.
And it seems you never really thought about these questions—how to reconcile them—and already jumped on others and called them stupid.
They’re stupid because they didn’t think that killing infants is immoral, and you’re not such a great genius either.
Because the excuses you wrote in that column—how does he not distinguish between prophecy and a situation without prophecy?—are not relevant.
What can you do? The Hebrew Bible explicitly says many times that such a reality exists.
True, his interpretation is very problematic.
But you also are not exactly the height of integrity. Indeed the topic is complicated, but your conclusions look problematic.
This iron rule—that you cannot learn moral truth from the Hebrew Bible—may be correct, but apparently you can learn from it about God’s attitude toward morality.