In considering the translation of נזר (nzr) as "holiness" or as "crown", is my thinking sound?
I think this is almost accurate, but I think there is an important distinction to be made. I wouldn't say that נזר (nzr) means either of those things, but rather it conveys the concept of something that is set apart or consecrated. "Crown" would be an appropriate translation in some contexts (Ps 89:39), but in other contexts it could be translated as "hair" (Jer 7:29) or "diadem" referring to the inscribed plate that was tied to a priestly turban, as some translations have understood it, e.g., Exodus 29:6 (
See note). It seems to be a context-dependent word that
could mean those things, but not necessarily.
Is τὸ ἁγίασμα simply "the thing that sets (a king) apart" or marks the king as set apart, i.e. the "crown"?
Interestingly, זר (nzr) could be translated as "crown" or "diadem" in Exodus 29:6 and the word used to translate it in the LXX is ἁγίασμά. Another important translation of ἁγίασμά, though, is a royal temple or sanctuary (Amos 7:13, here this is a translation for נזר (nzr)) In 1 Chron 28:10 and Dan 9:17, ἁγίασμά is also translated for "sanctuary" (מִקְדָּשׁ (miqdash)) Exodus 39:30 (LXX 36:37) translates the the inscription on the diadem: "῾Αγίασμα κυρίῳ·" "holy/holiness to the LORD." The NET understands ἁγίασμά to means "sanctity" in Psalm 93:5(LXX) and your own example Psalm 132:18(LXX). This seems to be in line with
LSJ which gives 2 possibilities for ἁγίασμά: 1) it equates it to ἁγιαστήριον, which means "holy place" or "sanctuary" or 2) holiness.
So to put it succinctly, I don't think it is accurate to say that τὸ ἁγίασμα means "crown" or "the thing that sets (a king) apart" in Ps 131:18 (LXX). I think it is fairly clear that this is an instance where there is not at 1:1 correspondence between the two words. It looks like the translator chose ἁγίασμα as the best word to replace זר (nzr) in the particular context, which interestingly does not seem to be translating as זר (nzr) as "crown".
Retaining νεζερ suggests that it was a technical term when used in Greek among the Jews of Alexandria, when speaking of the crown
I don't think this is necessarily true either. In fact, I think this is a very speculative conclusion, especially since we have seen זר (nzr) translated in other ways. If I were to speculate myself, I would say that the word זר (nzr) seems to have a nuanced meaning that is often dependent on context and circumstance. Instead of trying to translate it, the translator opted to just transliterate the word right into Greek. Often with the LXX you can see what appears to be evidence of different translators in different places, and some seem to be a little more competent at translating the text. There are definitely examples of awkward or incorrect word usages in the LXX for this reason. Because of this, it may also be difficult to generalize across the LXX. Additionally, I think it would be hard to identify νεζερ as a technical term for "crown" unless there is more evidence to back it up. So far, I can only find this one instance of the transliteration of νεζερ for "crown" here. I think we would need corroboration from other places before assuming that. I haven't checked extensively for other instances yet, but I would be interested to know if this transliteration happens in any other places.
I suppose someone may disagree with me, but that is how I would understand it.
