My thanks to Konstantinos Konstantinides, Joseph Boyle, and Jorvon M. Carter, who have answered most of this; this answer is based on their work.
My agenda, more cynically, was “which country did Greek copy, and where did it decide to do its own thing.” Languages did decide to do their own thing occasionally; the Russian (and hence Slavic) word for silicon, kremnij, for example, is a 1834 coinage based on Ancient Greek krēmnos, ‘precipice’.
For most of these, if Greek hasn’t patterned with English, it’s because it has patterned with the actual prestige languages of the time, French and German. My guess is, German unless German used a Germanic term, in which case, French.
- N: French (German has Stickstoff)
- Na: German
- K: German
If a Greek term was used early on and then abandoned, Greek would be delighted to hang on to the Greek term.
- F: Phthorion (suggested by Ampère in 1810)
- Zn: Pseudargyros was used by Strabo, and identified with Zinc. Greek was certainly not going to pass by a term with classical pedigree.
And for three elements, Greeks did their own translating:
- Pt: Greeks seems to have been desperate to avoid the Spanish Platinum; I’d have thought the 1752 description of it as a “white gold” would have been an obscure place to go, but clearly not obscure enough.
- Si: Pyrition “flint-ium” is a translation of the usual European term silic-ium.
- Al: Argilion “clay-ium”, based on the presence of aluminium in aluminium silicate, the basis of clay; aluminium in the West was instead named for alum, which also contains potassium. The decision by Greek to go a different way with the naming of Aluminium is puzzling; all the more so because Wikipedia cites the 1782 French paper by Louis-Bernard Guyton de Morveau, who first proposed the name alumine—and who expressly rejected a name like argilium as redundant:
“La seconde terre est celle qui sert de base à l’alun: en la nommant argille, il faudroit chercher un autre nom au minéral, qui n’en recèle jamais qu’une portion; il faudroit, suivant notre second principe, substituer le mot argilleux au mot alumineux, pour tous ses composés. Il est plus simple de conserver le dernier, & en tirer un substantif, pour indiquer l’étre primitif. Ainsi, l’on dira que l’alun ou vitriol alumineux a pour base l’alumine, que la Nature nous offre abondamment dans les argilles.”
(The second earth is what serves as the base in alum: by naming it “clay”, one would have to seek another name for the mineral, which never harbors even a part of it; one would have to, following our second principle [for naming chemical compounds], substitute the word “clay-ish” for the word “aluminous” in all its compounds. It is simpler to retain the latter and to draw a noun from it, in order to indicate the primitive entity [i.e., element]. Thus, one will say that alum or aluminous sulfate has as [its] base alumine [i.e., aluminium], which Nature offers us abundantly in clays.)
EDIT: from exchange with Joseph Boyle in comments, there’s one possibility for why Greeks avoided the literal translation styption of aluminium: alum, being an anti-bleeding agent, was a traditional remedy for, among other things, haemorrhoids. In fact, I remember thinking “there’s something disreputable about stypsis in Greek, and I can’t quite remember it”: that must have been what I was trying to remember.