(provisional repsonse)
Some equivalences between Pessach Rishon and Pessach Sheni. Mishna Pessachim 9, 3:
מַה בֵּין פֶּסַח רִאשׁוֹן לַשֵּׁנִי, הָרִאשׁוֹן אָסוּר בְּבַל יֵרָאֶה וּבַל יִמָּצֵא, וְהַשֵּׁנִי, מַצָּה וְחָמֵץ עִמּוֹ בַּבָּיִת. הָרִאשׁוֹן טָעוּן הַלֵּל בַּאֲכִילָתוֹ, וְהַשֵּׁנִי אֵינוֹ טָעוּן הַלֵּל בַּאֲכִילָתוֹ. זֶה וָזֶה טָעוּן הַלֵּל בַּעֲשִׂיָּתָן, וְנֶאֶכָלִין צָלִי עַל מַצּוֹת וּמְרוֹרִים, וְדוֹחִין {ז} אֶת הַשַּׁבָּת {ח}:
ר"ע מברטנורה וְהַשֵּׁנִי חָמֵץ וּמַצָּה עִמּוֹ בַּבָיִת. דִּכְתִיב (בְּמִדְבָּר ט) כְּכָל חֻקַּת הַפֶּסַח יַעֲשׂוּ אֹתוֹ, מַשְׁמַע מִצְווֹת שֶׁבְּגוּפוֹ, כְּגוֹן צָלִי וְעַל מַצּוֹת וּמְרוֹרִים יֹאכְלֻהוּ, עוֹשִׂין אוֹתוֹ כְּכָל חֻקַּת הַפֶּסַח[1], אֲבָל מִצְווֹת שֶׁעַל גּוּפוֹ מִמָּקוֹם אַחֵר, כְּגוֹן תַּשְׁבִּיתוּ שְׂאֹר וְלֹא תִשְׁחַט עַל חָמֵץ, אֵין עוֹשִׂין אוֹתוֹ כְּכָל חֻקַּת הַפֶּסַח:
עיקר תוספות יום טוב: אַף עַל גַּב דְּעַל מַצּוֹת וּמְרוֹרִים מִקְרָא מָלֵא הוּא בְּפֶסַח שֵׁנִי, הָ קָאָמַר, דִּכְלָלָא דִּכְכָל חֻקַּת וְגוֹ' מְרַבֶּה צָלִי, דְּדוּמְיָא דִּפְרָטָא דְּעַל מַצּוֹת וּמְרוֹרִים כוּ'
Hillel and Rabanan in Gemera Chapter 10, Daf 115A
Rabina said, R' Mesharsheya son of R'Nathan told me: Thus did Hillel) say on the authority of tradition: A man must not make a sandwich of mazzah and bitter herbs together and eat them, because we hold that mazzah nowadays is a Biblical obligation, whereas bitter herbs are a Rabbinical requirement and thus the bitter herbs, which are Rabbinical, will come and nullify the mazzah, which is Biblical[2].
And even on the view that precepts cannot nullify each other, that applies only to a Biblical [precept] with a Biblical [precept], or a Rabbinical [precept] with a Rabbinical [precept], but in the case of a Scriptural and a Rabbinical [precept], the Rabbinical [one][3] comes and nullifies the Scriptural [one].
Which Tanna do you know [to hold] that precepts do not nullify each other? - it is Hillel.
For it was taught, it was related of Hillel that he used to wrap them together, for it is said, they shall eat it with unleavened bread and bitter herbs.
R`Johanan observed: Hillel's colleagues disagreed with him.
For it was taught: You might think that he should wrap them together and eat them, in the manner that Hillel ate it, therefore it is stated, they shall eat it with unleavened bread and bitter herbs, [intimating] even each separately.
To this R`Ashi demurred: If so, what is [the meaning of] 'even'?
Rather, said R`Ashi, this Tanna teaches thus: You might think that he does not discharge his duty unless he wraps them together and eats them, in the manner of Hillel therefore it is stated, they shall eat it with unleavened bread and bitter herbs, [intimating] even each separately[4].
Now that the law was not stated either as Hillel or as the Rabbis, one recites the blessing.'
[Who hast commanded us] concerning the eating of unleavened bread' and eats; then he recites the blessing, 'concerning the eating of bitter herbs,' and eats; and then he eats unleavened bread and lettuce together without a blessing.
in memory of the Temple, as Hillel [did].
(Soncino's translation)
Nowadays, with Korech, may be that we can fullfill the mitsvat maror, but not Matsa and Hillel itself agrees to this.
(I need to learn this a little more)
[1] The Bartenura and Ikar Tosfot Yom Tov, as a digest of the Gemara says that the law extracted from a verse talking about Pessach Sheni is relevant for learning that we do eat Korban Pessach in presence of matsot and maror.
[2] Nowadays Hillel to agrees that we can not fulfill the Mitsvat Matsa through the Korech, despite that two Mitsvot deOrayta do not annullate one another.
[3] Maror is rabinical because nowadays, because we have not the Korban Pessach. Maror is a mitsva only to implement the korban pessach meal
[4] See Tosfot. According to tosfot, one may fulfill the mitsva with a korech following Hillel and Rabanan, the Machloket is Lechatechila. Despite that generally Mitsvot annulate one another according to rabanane, here it is different because a special mention of the verse that it is possible to eat together Matsot and Merorim