second night of sukkos: which bracha comes first, sukkah or zman?

Last week I mentioned the question posed to R' Ovadya regarding saying slichos before mincha: why should mincha not come first given that it is tadir?

R' Ovadya answered by citing the Shaagas Aryeh's (#22) view that the rule of tadir only applies when comparing apples to apples, e.g. a d'oraysa against another d'oraysa, or a derabbanan against a derabbanan.  It does not apply when comparing a minhag like slichos to a derabbanan.  

First let's explain this counterintuitive idea a little more, and then we will see how it applies to sukkos:

It's only once a person decides to engage in doing a mitzvah or mitzvos that we look at what is tadir or mekudash to determine which mitzvah takes priority. However, if you are not yet engaged in doing those mitzvos -- you instead choose to be involved in some reshus/mundane activity -- tadir or mekudash does not force you to stop.  The rules of precedence do not come into play.

Viz a viz a mitzvah doraysa, a derabbanan is considered a reshus.  Viz a viz a derabbanan, a minhag is a reshus.  Saying slichos before mincha would not be worse than playing a game of baseball before mincha -- since you are not yet engaged in a mitzvah activity, the rules of precedence do not apply.

Shaagas Aryeh brings the following proof: the gemara (Brachos 51) quotes a machlokes Beis Shamai and Beis Hillel as to which bracha to say first in kiddush, the borei pri ha'gefen or the bracha on the kedushas ha'yom.  We pasken like B"H that the bracha on the wine comes first.  

Kiddush ha'yom is a mitzvah d'oraysa, it's mekudash.  How can you say the bracha on wine before doing the mitzvah d'oraysa?  

QED, that putting a reshus before a d'oraysa is not an issue.

The Tzlach takes exception to this proof and writes that the case in the Mishna is where one already davened maariv and was yotzei the mitzvah d'oraysa of kiddush in tefilah -- the case of the Mishna is where both brachos are derabbanan.  Had there been a bracha obligation that stemmed from a mitzvah d'oraysa, it would indeed have to come first.

(This Tzlach gives rise to the famous question he asks l'shitaso: if a man davened maariv and already fulfilled the d'oraysa of kiddush, how can he be motzi his wife who has not?  A discussion among Achronim for another time.)

Coming now to sukkos, on the first night we first say the bracha of sukkah first and then the bracha of zman because we want the she'hechiyanu to apply to both the mitzvah of sukkah and the kedushas ha'yom of sukkos.  However, the S.A. writes (O.C. 661) that on the second night we reverse the order and the bracha on zman comes first and then the bracha on sukka.  Rama tacks on that he concurs.  (Interesting -- the Rama usually tells us when he disagrees with the mechaber; here he goes out of his way to tell us that agrees, as if we would suspect that he doesn't.) On the second night the bracha of zman applies only to the kedushas ha'yom but not to the mitzvah of sukkah, as the she'hechiynu on sukkah can be said even before the chag.  

The Raavyah disagrees.  Raavyah writes that that zman always comes at the end.  He compares it to yakniha"z -- when a Y"T falls on motzei shabbos, we say kiddush and havdalah together and then tack on zman at the end even though the she'hechiyanu has nothing to do with havdalah and really belongs with kiddush.  So too on sukkos, even though zman has nothing to do with sukkah, it still comes at the end.

(One could argue that kiddush and havdalah are inseparable because both are brachos on kedushas ha'yom.  The Rambam, for example, holds that havdalah is a mitzvah d'oraysa that is learned from the same pasuk as kiddush.  Sukkah and kedushas ha'yom do not have that same relationship.)

Noda b'Yehudah (#39) / Tzlach paskens like the Raavyah and l'shitaso offers l'shitaso another reason for zman to come at the end: the bracha on sukkah is a bracha on a d'oraysa and therefore is considered mekudash and takes precedence over the bracha derabbanan of zman.  No different than would be the case if in theory the bracha on kedushas ha'yom in kiddush was d'oraysa, in which case it would take precedence over the bracha on wine.

Just for the record, here's the Rambam's psak (hil lulav 6:12):

ובלילי יום טוב הראשון מברך על הסוכה ואחר כך על הזמן. 

On the one hand, he says ום טוב הראשון implying the second night is different.  On the other hand, when he says ובלילי in the plural, does he mean to include the second night, which is really night #1 if we take sfeika d'yoma into account?  

The Aderet has a brilliant proof that the Raavyah is right.  He dug up a Yerushalmi in Brachos (57b, ch 8 halacha 1):

 יום טוב שחל להיות במוצאי שבת ר' יוחנן אמר יקנ"ה יין קידוש נר הבדלה חנין בר בא אמר בשם רב יין קידוש נר הבדלה סוכה וזמן.

The Ylmi can't be talking about the first day of sukkos on a motzei shabbos because 1) we have a rule "lo AD"U Rosh" that says Rosh haShana cannot start on a Sunday, so neither can sukkos which falls out exactly two weeks later; 2) we have another rule that hoshana rabbah never falls on Shabbos, so sukkos cannot possiblt start on Sunday.  Therefore, the Ylmi is must be speaking about the second day of Y"T and Ylmi holds that zman comes at the end, after the bracha of sukkah.

Amazing bekiyus.