Dear Rabbi Kornfeld, Your answer (b) as to why Besamim precedes Ner, since Besamim is Tadir because we recite blessings for Besamim throughout the week, could be problematic according to Zevachim 91(a) which says that the rule of Tadir is ' Tadira Bemitzvos', that the freqency is tied to obligations rather than being optional (see Artscroll notes to 51b regarding Tadir). Rav Simcha Kook, Rav Harashi of Rechovot, to give you some support, mentioned that perhaps since Sephardim make a bracha over Besamim for a Bris, this would lend itself to Mitzva.
A Rav Elimelech Winter pointed out to me the Aruch Hashulchan (siman 296:6) who, in support of your position, also uses Tadir by Besamim. I assume the Aruch Hashulchan didn't see Art Scroll's comments on 51b.
Yashar Koach! Thank you very much for bringing to our attention the issue of Tadir applying only to Mitzvos, and for showing us the Aruch ha'Shulchan. I might just add that the Chasam Sofer (OC 225:3) applies the rule of Tadir to his ruling that the blessing of ha'Etz precedes that of She'he'cheyanu, which is an application of Tadir in a case other than Mitzvos.