Of Seders and Sandwichs

Every year at the seder we reach a part called korech where we put some marror on the matzah, announce that we're making like Hillel in the times of the Temple and then eat the stuff.  But two good questions could be asked about this:
1) Why make the sandwich in the first place after eating the matzah and marror separately
2) Why mention Hillel?  If the Rabannan disagreed with him, why are we following his custom?  And if they agreed, why mention him?
In fact, in the Mishneh Torah, hilchos Chametz U'Matzah, 8:6-8, the Rambam goes through the routine of korech and mentions zecher l'mikdash without mentioning Hillel, implying that everyone does agree you should eat the sandwich.
The Talmud in Pesach 114a says:
Rabhina said: R. Mesharshia the son of R. Nathan told me, that so said Hillel, quoting a tradition: A man should not place the bitter herbs between unleavened cakes and eat them in that manner. Why not? Because the eating of unleavened cakes is a biblical commandment, while the eating of bitter herbs in this day is only a rabbinical ordinance. Now if the two be eaten together, the bitter herbs might destroy the taste of the cakes, and thus a rabbinical ordinance would supersede a biblical commandment; and even according to those who hold that one commandment cannot nullify another when both are fulfilled at the same time, such is only the case where both are biblical or both are rabbinical; but when one is a biblical and the other a rabbinical commandment, the rabbinical nullifies the other, and hence their joint fulfilment is not allowed.
Who is the Tana from whom we have heard that the fulfilment of one commandment does not nullify that of another? That Tana is Hillel, as we have learned in a Boraitha: It was said of Hillel, that he would take a piece of the paschal offering, an unleavened cake, and some bitter herbs, and eat them together, as it is written [Numb. ix. 11]: "With unleavened bread and bitter herbs shall ye eat it."
R. Johanan said: "Hillel's colleagues did not agree with him, as we have learned in a Boraitha: Lest we assume that the paschal offering, the unleavened bread, and the bitter herbs must be eaten together, therefore it is written, 'With unleavened bread and bitter herbs shall ye eat it,' which signifies, that each may even be eaten separately." R. Ashi opposed this: "If this Boraitha is supposed to be in opposition to Hillel, why does it state that each may even be eaten separately? (If they may be eaten even separately, then surely they may be eaten together.) Therefore the Boraitha means to state, that even if the three things were eaten separately the duty was acquitted, though they should rather be eaten together."
Now in this day, when it is not known whether the Halakha prevails according to the opinion of Hillel or of the opposing sages, the mode of procedure should be thus: A blessing should be said over the unleavened bread and a piece thereof eaten; then another blessing should be said over the bitter herbs and a piece tasted, and finally the unleavened bread and the bitter herbs should be put together and eaten at the same time, saying: "This is in remembrance of Hillel's actions when the Temple was still in existence."
Harav Shaul Yisraeli, zt"l, brings the following analysis of the sugya in his work Chavos Binyamin:
The Rashbam says the gemara brings three opinions on the eating of pesach, matzah and marror.
1) Hillel holds that mitzvos ein mevatlos zeh es zeh so we eat all three together in a sandwich
2) The Rabannan hold that the unusual word yochluhu used instead of the more common yochlu implies a plural - you can eat them separately or together and both ways you fulfill the mitzvah
3) The Rabannan according to Rabbi Yochanan hold that mitzvos mevatlos zeh es zeh and therefore we must eat all three separately.
According to Tosafos on 114a, there are two opinions:
1) Hillel holds that it's ideal to eat all three as a sandwich but the word yochluhu means it's not essential.
2) The Rabannan hold that each can be eaten separately but also together because the principle mitzvos mevatlos zeh es zeh does not apply in this case.
Now, it's important to remember that the seder in Temple times was significantly different from post-Temple times because of the presence of the paschal offering and all the rules surrounding it.  Nowadays in its absence matzah still has a d'oraysa obligation associated with it because the Torah gives it a separate one independent of the Temple but marror is only eaten d'rabannan.  How does this play out?  If we were to eat the matzah and marror together right off the top, the Torah-level matzah would mevatel the Rabbinic level marror, interfering with fulfilling the two oligations.  So we eat them separately, each with their own blessing and then announce zecher l'Mikdash without making a further blessing.
However, according to Rambam, in the times of the Temple the routine was different.  According to him, the procedure was as follows:
1) Take the matzah and say  HaMotzi, then eat some
2) Take matzah and marror and say Al achilas matzah u'maror and then eat it
3) Take the paschal offering, say al achilas Pesach and eat it.
One of the problems with this is that the gemara says that in Temple times we say al achilas maror right after the borei pri ha'adamah earlier one because after filling one's belly with marror, it makes no sense to then say al achilas maror.  This should apply to matzah too.  Having said hamotzi and eaten some, how can you then say al achilas matzah?
Further, the Rambam's order is difficult.  First say hamotzi and eat some matzah, then say al achilas matzah and eat some more?
Now, according to Tosafos elsewhere mitzvos tzrichos kavannah which means I can eat the vegetable earlier on in the seder and have in mind that I am not fulfilling my obligation to eat marror and it is of avail.  However, Rambam holds that mitzvos do not require kavannah so eating the matzah after hamotzi fulfills my specific obligatoin to eat matzah even if I don't have it in mind. 
The Rambam therefore holds that in Temple times the sandwich isn't just a preferred option, it is the obligation.  By eating matzah separately I do not fulfill the obligation of the verse al matzos u'merorim tochluhu so eating the matzah after hamotzi is not a problem.  According to Rambam, even if one eats the matzah and marror separately first, one can still make the blessing al achilas matzah u'maror on the sandwich because this is the actual obligation which has not been fulfilled yet.
But then Rambam says that the paschal offering is eaten separately after the sandwich while the gemara implies that both Hillel and the Rabannan hold that it should be eaten together with them.  How does one reconcile this difference?
Rav Israeli explains that the Rambam has a unique way of understanding the sugya that goes in a different direction from what we have been assuming until now.  Remember that he says that the sandwich is zecher l'mikdash but doesnt mention Hillel.  Why?
Until now we have assumed that the issue of whether or not mitzvos mevatlos zeh es zeh revolves around what happens when you mix matzah and marror.  The Rambam holds that this is, in fact, not the basis of the dispute.  Rather the dispute is over whether or not to mix the paschal offering with the matzah-marror mix.  This is because the verse al matzos u'merorim yochluhu obliges us to mix the matzah and marror together so the whole mitzvos mevatlos zeh es zeh doesn't apply to it.  Therefore the gemara is discussing an argument between the Rabannan who say you can`t mix the paschal offering with the sandwich because mitzvos mevatlos zeh es zeh and Hillel who says you can because mitzvos don`t mevatlos zeh es zeh.
Rabbi Yochanan understands the argument as being over whether one can put the paschal meat in the sandwich or not.  Rav Ashi, on the other hand, understands the Rabannan as not only agreeing that one can put the paschal meat in the sandwhich but that there is a chiyuv to do it in the first place.
All this applies to Temple times but nowadays, as noted before, matzah is a Torah level obligatoin and marror is only rabbinic and everyone agrees that mitzvos mevatlos zeh es zeh.  This means we have to say hamotzi and al achilas matzah sequentially because we also hold mitzvos einam tzrichos kavannah.  Afterwards, like the gemara says, we say zecher lMikdash  as a reminder of the previous procedure when our Temple (may it be speedily rebuilt) was standing.  According to Rabbi Yochanan, this follows the view of Hillel but since the Rambam says everybody holds this way, he does not include the name of Hillel in his hagadah since there is no need.