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

1) I think the key may be to understand the source of the phrase "Gomrim Alav Es ha'Hallel" that Rashi uses.

2) This phrase occurs in Erchin 10a which lists the 18 days in the year that an individual is "Gomer ba'Hen Es ha'Hallel" (One of these days is the first day of Pesach, so according to Rashi here in Pesachim we can say now that this also includes the first night.)

3) The Rambam (Hilchos Chanukah 3:7) writes that saying Hallel on Rosh Chodesh is only a custom and therefore one leaves out parts of the full Hallel. Accordingly, it seems that the main intention of Rashi in Pesachim 36a, when he writes that one completes Hallel on Seder night, is to stress that Hallel on Seder night is not merely a custom but is in fact a full obligation.

4) According to this, the crucial thing is not whether one says the entire Hallel when the Matzos are still on the table. Even if one ate the Matzos in the middle of the Hallel, it is still considered as though he was Gomer Es ha'Hallel on the Matzos, because he said part of the Hallel when the Matzos were there, and, in addition, he said later the entire Hallel, so this is sufficient to be considered as though he completed the Hallel on the Matzos.

5) There are different reasons why one splits up Hallel and says part of it after the meal. See the Mordechai (page 66, column 2, in the back of the standard editions of the Gemara), who writes that we want each of the Four Cups to be associated with something special, and since otherwise the second cup would not be connected with any outstanding feature, it was given the first part of Hallel which one says before drinking the second cup, and the remainder of Hallel was designated for the fourth cup. However, this latter detail is a side matter, but the main point that Rashi is making is that we say the full Hallel on Seder night.

6) We can sharpen this point slightly by pointing out that there are opinions in the Rishonim which maintain that it is a Torah Mitzvah to say Hallel on Yom Tov (see Kesef Mishneh, Hilchos Chanukah 3:6, in the name of the Behag). The Kapos Temarim comments (on Tosfos to Sukah 38a, DH Mi) that the opinion of Rashi is also that Hallel is a Torah Mitzvah. The Kapos Temarim does not cite our Rashi in Pesachim, but we can now suggest that when Rashi writes that one completes the Hallel on Seder night he is stressing the high level of the Mitzvah of saying Hallel at this time.

7) We can also add another source which may illustrate slightly that it is not necessary to literally have the Matzos in front of us for the entire reading of Hallel. This is from Rashi in Chumash in Bamidbar 2:20. The Torah states there that the tribe of Menasheh were "Alav" of the camp of Efrayim. How can it be that the tribe of Menasheh is "on" the camp of Efrayim? Rashi there cites Onkelos that this means that Menasheh was near Efrayim, not literally on top of Efrayim. We may now suggest that when Rashi in Pesachim writes that one completes the Hallel "Alav" the Matzos, this means that one says Hallel "near" the Matzos, but it is not necessary that the Matzos should be there for the entire Hallel.

8) However, the latter observation is not essential, but the main point is that the complete, high level of Hallel is said at the time the Matzos are eaten and it is not necessary for the Matzos to be present for the entire recitation of Hallel.

(See also Chidushei Mishneh, by Rav Menasheh Klein zt'l of Ungvar, to Rashi Pesachim 36a.)

Kol Tuv,

Dovid Bloom