Of course, it's upsetting.
Especially when these young girls are all innocent right? Wrong.
This is the point.
Let's discuss the range - 3 years to 12 years. Children can be indoctrinated very easily. They are used today in the most horrific ways - slave labor, fighting in wars. It is estimated according to Reuters that 350 million children worldwide are used as soldiers. This is today, yes, 2018. Horrific!
My point is to illustrate that your assumptions about innocent girls is simply based on your own moral compass. I agree that all things being equal killing small children for fun, is morally reprehensible. Period. I totally agree. Can small children be redeemed - can they repent from their ways. I would venture to say that the answer might be an emphatic no.
In terms of today, child soldiers could possibly be, sadly, irredeemable. A child's experiences, especially in the formative years, affects brain chemistry, and reforming them, might be an altogether impossible task. It is not a simple matter of simply 'converting people'. We're talking dedicated indoctrination of principles that antithetical to moral culture. We see this today in the cycle of hatred of various groups calling for the destruction of Israel and do not recognize the Jewish state. This is inculcated very early on, and children assume this to be the truth, and do not question it.
This is going on today.
Back to the Torah. The Torah is talking about a spiritual issue that cannot be corrected, and must be eradicated. We don't make these judgments, G-d does. We see very clearly, that the Jewish people were not happy to do this, and had to do be told a second time to carry out the act. We were told to do it by G-d.
In sefer Hayashar it is brought that the Egyptians buried children in the walls. Moshe Rabbeinu has a complaint directed at Hashem for doing this, and as a result, Hashem allows two to be saved to show Moshe what becomes of these children. They become the leaders of the Eiruv Rav and become extremely wicked people (see Rokeiach Beshalach 14-11). We see from a spiritual perspective G-d saw that these children are not going to be redeemed nor are redeemable. They must be removed from this world. Again, G-d makes these decisions. We don't.
We see death and being killed by the sword as being negative and destructive. However, we also know that one of the punishments of Beis Din is Saif (death by sword). Punishments meted out by Beis Din are not punishments in the sense of correction. If G-d wanted to, He could have done things differently. The point about the punishments so that we end up in the World to Come. They are there to help us fix the mess we made in this world. Death is a neutralizer of our many failings and sins.
While we see that death and destruction, especially of small children is completely at odds with our western sensibilities; nonetheless, if we change our perspective of what is going on here, we understand that things aren't always as they seem, and that we're open to different views and we question our assumptions, we will find that the Torah's understanding is the correct moral approach.