"To put it more provocatively, the usage here seems to be eisegesis or, perhaps, prooftexting".
Conclusions like these result from the assumptions brought to the text.
In a literal interpretation it is presumed that Ps 2 speaks of one thing, of which the human author was aware. Therefore, when a NT author finds something more, we presume it is eisegesis, prooftexting, or even as some authors suggest, wishful invention.
In a sensus plenior interpretation, a literal meaning is acknowledged, but so are three hidden meanings, two of which speak of Christ. Since it is presumed that it is God's intention to speak of Christ, then a conclusions of eisogesis, or prooftexting are unwarranted.
If a hammer keeps bending nails no matter who uses it, then take a closer look at the hammer. If the issues which arise from a literal approach to the scriptures keeps causing exegetical problems, then perhaps it is the approach which is the problem.
The author of Hebrews is the one who says it applies to Jesus. Presumably he is more of an authority on the topic than any modern interpreter. It would seem reasonable to take a closer look at the hammer.
Should we try to use the same methods as the apostles? Considering that they were specifically instructed to teach us, and they said we should imitate them, it just seems natural that their use of the Old Testament should be considered normative rather than exceptional.
--Addition--
The hermeneutical approach used by the author is used throughout the NT and is used by Paul in Galatians and is one of the rules of interpretation by Rabbi Eliezer ben Jose H'G'lili, the second Century teacher of hermeneutics. It is the rule of Mashal, or that of parable. The OT history is taken as a parable of Christ. Jesus said all the scriptures spoke of him.
Paul uses it in Galatians speaking of two women who represent grace and law. His doctrine, that where there is law, there is no grace comes from the parable in the blessing of Essau.
Ge 27:40 And by thy sword shalt thou live, and shalt serve thy brother; and it shall come to pass when thou shalt have the dominion, that thou shalt break his yoke from off thy neck.
Esau also representing law serves grace, represented by Jacob. The law will serve grace... the law is a schoolmaster to lead you to the grace of Christ, and when the law has dominion, there is no grace.
This is the hidden layer of the OT scripture.
Speaking to the OP: the characters in a parable can be replaced by their ante-type and then the riddles can be exposed and solved.