David Hamelech and His 400 Children?

From Rav Shmueli's newsletter from last week (p. 14):

Sanhedrin 21a:

Rav Yehuda said in the name of Rav: King David had 400 children who were all children of "Yefat To'ar" women, and they grew their hair as a Belorit and they all sit on golden wagons and they travel at the front of the army. And these were the strongmen of the house of David.

Rashi in Kiddushin 76b explains that it means children born to members of his army, and they remained non-Jews, which is why they kept their Belorit hair-style, a style forbidden to Jews. However, the problem with this explanation is that the gemara in Sanhedrin implies that they were actually David Hamelech's children. So, besides the obvious question of how David Hamelech can have so many children, we have another issue in that a warrior is halachicly entitled only one Eishet Yefat To'ar per war (Rambam, Hilchot Melachim 8:3) and we know that David Hamelech only waged 18 wars (Vayikra Rabba 1:4). If so, how is this halachicly possible for David Hamelech to do so, and why wasn't this story of David Hamelech noted as a question when the gemara in Kiddushin 22a mentioned the 1-Yefat-To'ar-per-war halacha?

The Yad Ramah is also bothered by the question and he says - similar to Rashi - that it must be referring to 400 men with 400 Yefat To'ar women - or less than 400 if they had twins. He agrees that it cannot be referring to David Hamelech's actual children since Yefat To'ar status is only at the first Bi'ah, and if there was Bi'ah afterwards, she would be considered a Giyoret - not a Yefat To'ar - and furthermore, he would thereby have more than 18 wives, so it must be referring to other men.

The Ben Yehoyada asks on Rashi's explanation: why did they not convert? And if they did convert, why were they allowed to keep their Belorit hair-style? He says, therefore, that really, they did convert, but were allowed to have a Belorit since the prohibition to have a Belorit is only Rabbinic and in a wartime setting, it was permissible since these men were used to scare the enemy. They were put at the front of the battle to show the enemy that in previous wars, the Jews were victorious, and captured many Yefat To'ar women, who had these Belorit-styled men as sons. They needed a Belorit to distinguish them from other Jews since the enemy knows that Jews don't have Belorit styles, so they must be from Yefat To'ar women. The reason why there were exactly 400 of them is to counteract the Sitra Ahara, which is the Sod of Esav coming with 400 men.

Rav Reuven Margoliot [couldn't find the source, but found it also quoted here] has a somewhat radical solution to the problem. He says that from the verses at the beginning of Divrei Hayamim Alef, chapter 3, it lists 6 sons of David Hamelech and their mothers, 4 sons and their mother, and then it lists 9 sons without their mother. It was these 9 sons whose mothers were Yefat To'ar women. When the gemara says "400 children", this was a scribal error since the original scribe wrote ת' to denote תשעה for 9, but the copyist assumed it was ת' for 400.

Rav Shmueli concludes that even though Rav Margoliot's solution is interesting, other commentators didn't hold like it and explained the 400 literally [whereas Rav Margoliot is explaining "his children" literally, while the other commentators do not].

Rav Shmueli then goes on about another one of Rav Margoliot's amazing explanations - the 12 wives of Bar Kappara.