At the very least, I think that weighing all the data, it’s best not to say that the reading of “son” is simply Christianizing the text. It’s a translation that takes the text as it is written and translates it in a syntactically normal way. As you say, the options all have problems, and “That’s why folks reconstruct the text.” We wouldn’t see the versions that say “feet” if it were all that easy to understand בר as an adverb meaning “with sincerity”.

I also don’t quite look at it the way you do when you say that בר for “son” would be a “stray Aramaic word.” We find Aramaic vocabulary all over the OT, just like we find Latin vocabulary all over our own English writing. I wouldn’t say that my use of the word “vocabulary” just now was a stray Latin word. As a student of the cognate literature of the OT, do you also say that Persian, and Akkadian vocabulary found in the Bible are stray words? Is בר in Prov 31:2 isa stray Aramaic word? And if all the Aramaic vocabulary that we find in supposedly Hebrew works is a bunch of stray Aramaic words, then we’ll get into real trouble when we progress later and later in the Hebrew language, where the Aramaic vocabulary piles up considerably more. If the author of Psalm 2 did mean בר in the same sense in which he had just used בנ, then in his mind he was merely using two synonymous words, not inexplicably changing languages.

Also, בר as “pure” doesn’t generally mean ritual purity, at least not in the examples I’ve skimmed over in the course of this discussion.

You’re right, so far as the Priestly traditions care. They use טהר. However, for those who want to posit Ps.2 is early, Ugaritic evidence can come in to play where brr occupies a similar semantic range as קדש in the HB.

But since the substantival meaning of בר can only be “pure one” and never “purity,” I just don’t see how an adverbial accusative can make sense.

That’s why folks reconstruct the text

It surprises me that HALOT would opt for “son,” but I still don’t think it works.