Succah 10b - Osek B'mitzvah D'rabonon

The gemara cites a machlokes between R. Nachman  and R. Chisda regarding decorations that hang more than 4 tefachim below the roof, whether it invalidates the Succah. Although R. Chisda and Raba Bar Rav Huna held that it does invalidate the Succah, when they were travelling to visit the Reish Gelusa for the Yom Tov they slept in such a Succah. Their rationale was that although in their opinion the Succah is passul, they were שלוחי מצוה and therefore exempt from sleeping in a Succah. Rashi comments that they were considered shluchei mitzvah because they were going to greet their rebbi  - שלוחי מצוה אנן, להקביל פני ראש גולה, דחייב אדם להקביל פני רבו ברגל. It is unclear to me why rashi needs the additional phrase of דחייב אדם להקביל פני רבו ברגל. Does Rashi mean to say that since chazal instituted that one must visit his Rebbi on Yom Tov (Rosh Hashana 16), therefore it was considered a mitzvah to exempt from succah but had there not been a specific obligation to go then it would not exempt. Or does rashi mean to simply say that we see from there that there is a mitzvah involved in visiting one's rebbi so regardless of when goes to visit their rebbi they would be exempt from other mitzvos that come their way? It seems from Rashi that it was specifically because there was an obligation at that time to visit one's rebbi that they were able to go knowing that they would likely miss out on the mitzvah of succah, otherwise they should have waited and gone a different time.

In my sefer Nasiach B'Chukecha (pg. 63) I have a discussion whether we say עוסק במצוה דרבנן exempts one from a mitzvah d'oraysa. I quoted that Rav Eliyashiv cites our gemara as a proof that even a mitzvah d'rabonon exempts from mitzvah d'oraysa, because greeting one's Rebbi is only learned מדברי קבלה, yet it is apparently considered a mitzvah to exempt from Succah. Today I found that the Mitzpeh Eisan makes exactly the same point. He draws a parallel from the gemara in Sanhedrin 70 where the gemara says that if a ben sorer u'moreh eats meat that is assur m'drabonon he doesn't become a ben sorer u'moreh. The gemara explains that the pasuk says ואיננו שומע בקולנו, he doesn't listen to the voice of his parents implying that that is the only voice stopping him from eating the meat - לאפוקי האי דאף בקולו של מקום איננו שומע. Just as in that context we regard an issur d'rabonon to be like a d'oraysa and it doesn't qualify as קולנו, so too by osek b'mitzvah which is learned from בלכתך בדרך - בלכת דידך, to exclude a mitzvah, an mitzvah d'rabonon would also qualify as a mitzvah.
The Ya'avetz is medayek from Tosafos that they disagree with Rashi. Tosafos writes - שלוחי מצוה אנן, וכגון שהיו מתבטלים מן המצות אם היו מחזרין אחר סוכה אחרת, that the mitzvah they would have lost was not merely the mitzvah of greeting their rebbi, but other mitzvos. If greeting their rebbi was the only mitzvah they would have lost, they would not be exempt from succah. Tosafos implies that there were other mitzvos that were presumably d'oraysa that they would have lost out on, had they made the effort to sleep in a succah.

Nonetheless, in my sefer I pointed out that from this proof we only see that a mitzvah d'rabonon which is a kiyum of  a d'oraysa such as honoring a Rebbi, exempts from a d'oraysa mitzvah. But we still don't see that a pure d'rabonon which is not at all a kiyum of a d'oraysa would exempt from a d'oraysa obligation.