(Please forgive the delay in response. Technical problems prevented the mailing of a number of responses.)

1) I have found an answer for why it is not sufficient to eat Matzah before the Korban Pesach. This is from Sefer Mikra'ei Kodesh, Pesach, part 1, by Rav Tzvi Pesach Frank zt'l, page 80 in the name of Rav Yakov Kalmas zt'l.

It is because the reason why the Korban Pesach must be eaten "Al ha'Sova" is so that one should not come to break the bones of the Korban Pesach since one is hungry to eat the meat. Therefore, if one should become satisfied by eating Matzah beforehand, one might still be hungry to eat meat and be tempted to break the bones, while if one eats meat before the Korban Pesach one will not be hungry to eat meat and will not come to break the Pesach bones.

2) As for why Chulin meat is not eaten to fulfill "Al ha'Sova," I have found (with the help of a fine Talmid Chacham in our Beis Midrash) an answer based on what Rav Chaim Solovetchik zt'l wrote (although he does not relate explicitly to your question).

a) Your question is sharpened if one looks at the Gemara in Menachos (21b) which states that when Kohanim eat Kodshim, they should eat Chulin and Terumah together with the Kodshim so that the latter should be eaten "Al ha'Sova." So the obvious question is, why then can Chulin meat not be eaten also before eating the Korban Pesach so that the latter will be eaten on "Al ha'Sova"?

b) This question can be answered if we look at what Rav Chaim writes (page 167 of the old ("stencil") editions, among the Chidushim on Maseches Pesachim, in the paragraph, "the Din of eating Pesach Al ha'Sova"). He asks, what is special about the Din that the Korban Pesach is eaten "Al ha'Sova"? After all, we see in Menachos (21b) that this Din applies to all Kodshim, and not merely to Pesach!

c) Rav Chaim answers that there are two Dinim involved in the requirement of eating "Al ha'Sova":

-The Din that all Kodshim are eaten "Al ha'Sova."

-The Din that the Korban Pesach is eaten "Al ha'Sova."

The difference between these two is that the first is a Din that applies only to Kohanim, while the second applies to any owners of the Korban Pesach, even if they are not Kohanim.

d) The proof for this is that otherwise it would not make sense how one can eat the Korban Chagigah before one eats the Korban Pesach. If "Al ha'Sova" would be a Din on all Korbanos, then how does one fulfil this when one eats the Chagigah before he is satisfied? We see that with the exception of the Korban Pesach, there is no Din of "Al ha'Sova" when a non-Kohen eats Kodshim.

e) Now we understand why the Gemara in Menachos (21b) says that the Kohanim should eat Chulin and Terumah before they eat the Korban. This is because they could not eat a Korban first before they eat the second Korban, because they would thereby miss "Al ha'Sova" for the first Korban. In contrast, when it comes to the owners of the Korban Pesach eating something before the Pesach, it is possible for them to eat a Korban Chagigah, because when the owners eat the Chagigah there is no Din of "Al ha'Sova."

f) The idea behind this is that it is preferable, if possible, to eat a Korban first to enable one afterwards to eat the second Korban "Al ha'Sova." This is a more honorable way of eating Korbanos in the Beis ha'Mikdash, so that all the food eaten there should be holy if possible, and is better than eating Chulin. However, when Kohanim eat Kodshim, there is simply no choice but to fulfill the Din of "Al ha'Sova" by eating something other than Kodshim, as explained above. In contrast, when it comes to eating the Korban Pesach, it is possible to fulfill "Al ha'Sova" by eating a Korban, and this is why the Chagigah is preferred to Chulin meat.

g) See also Sefer "Daf Al ha'Daf" on Pesachim, on this Sugya.

3) I later posed this question to a Gadol and he replied briefly, "There is only a Mitzvah."

I think this fits with the answer I gave above. We want the food that is eaten before the Korban Pesach to be food of a Mitzvah, and that is why it should be this special Korban Chagigah, which -- even if it is not an obligation -- is at least a Mitzvah. We would like to eat the food of a Mitzvah before other Korbanos as well but it is not possible to do this because they are eaten by Kohanim, as explained above, and therefore the first Korban also would have to be eaten "Al ha'Sova." However, with the Korban Pesach, where we do not have this problem, we revert to the general principle that it is always preferable that all things eaten as part of the Avodah in the Beis ha'Mikdash should be a Mitzvah, which is why the Chagigah is eaten before the Korban Pesach.

Kol Tuv,

Dovid Bloom