Hallel at the Seder

Yerushalmi Megilla 2:1 (18b)

משנה:

הקורא את המגילה למפרע לא יצא קראה על פה קראה תרגום בכל לשון לא יצא אבל קורין אותה ללעוזות בלעז והלועז ששמע אשורית יצא:

גמרא:

דכתיב (אסתר ט) ככתבם 

קראה על פה לא יצא דכתיב ככתבם קראה תרגום לא יצא דכתיב ככתבם: בכל לשון לא יצא: דכתיב ככתבם וכלשונם 

ר' יונה אמר תנה נחמן בר אדא ר' יוסה אמר תנה נחמן סבא (דברים ו) והיו כדרך הוייתן יהיו ותני אף בהלל ובקרית שמע המגילה כן ניחה בקריאת המגילה דכתיב ככתבם ברם בהלילא בגין דכתיב (תהילים קי״ג:ג׳) ממזרח שמש עד מבואו מהולל שם ה' מהולל שם ה' ממזרח שמש עד מבואו מה את שמע מינה א"ר אבין עוד היא אמורה על סדר 
- בצאת ישראל ממצרים לשעבר 
- לא לנו ה' לא לנו לדורות הללו 
- אהבתי כי ישמע ה' לימות המשיח 
- אסרו חג בעבותים לימות גוג ומגוג 
- אלי אתה ואודך לעתיד לבא

Interpretation:

Mishna:One who reads the Megilla out of order does not fulfil his obligation....Gemara:(An interpolation from the Talmud Bavli:  In the case of Krias Shema, we know the source for the requirement to read it in order, and that is the words) V'hayu, which we understand to mean "exactly as written in the Torah."The rule of our Mishna, stated regarding Megilla, applies as well to Hallel and Krias Shema.(Returning to Yerushalmi:)In the case of Megilla, because it states Kiksavam, meaning "as written."What is the source for requiring Hallel to be read in order?Because it says "From place to sun rises to where it sets, God's name is praised."  This implies that order is essential, to begin from the beginning and proceed to the end.Another proof: Because the concepts expressed in the Hallel are written chronologically:B'tzeis refers to the redemption from Egypt.Lo Lanu speaks of our time in the current exile.Ahavti speaks of the time after Mashiach comes.Isru Chag is the days of Gog u'Magog.Eili Attah is the ultimate and final goal of the future.

With this Yerushalmi, we understand why Hallel is split at the seder, with the first half before the meal and the second half after.

The first half sings of the redemption from Egypt, and then prayerfully speaks of our condition as free men who await the return of the Shechina and all of Klal Yisrael to the land, and asks Hashem's protection during our exile.  After we finish "Pesach, Matza, and Maror," the Hallel after the meal deals with the future God promised us, and although the wait seems endless, we sing about the wonders and joy that we will all experience when God fulfils His promise.

See also Bavli Pesachim 118 on the same topic.

 וכי מאחר דאיכא הלל הגדול אנן מאי טעמא אמרינן האי משום שיש בו חמשה דברים הללו יציאת מצרים קריעת ים סוף ומתן תורה ותחיית המתים וחבלו של משיח 

- יציאת מצרים דכתיב בצאת ישראל ממצרים 

- וקריעת ים סוף דכתיב הים ראה וינוס 

- מתן תורה דכתיב ההרים רקדו כאילים תחיית המתים דכתיב אתהלך לפני ה׳ 

- חבלו של משיח דכתיב לא לנו ה׳ לא לנו--

--ואמר רבי יוחנן לא לנו ה׳ לא לנו זו שעבוד מלכיות 

--איכא דאמרי אמר רבי יוחנן לא לנו ה׳ לא לנו זו מלחמת גוג ומגוג 

Steinzaltz interpretation, from Sefaria - 

And since there is the great hallel, which contains the special praise of “Who gives food to all flesh” (Psalms 136:25), as explained above, what is the reason that one also recites this hallel of Psalms 113–118, the section recited on every joyous occasion? The Gemara answers: The reason is because the regular hallel contains these five matters: The remembrance of the exodus from Egypt, the splitting of the Red Sea, the giving of the Torah, the resurrection of the dead, and the pangs of the Messiah. Since it mentions these key concepts, this hallel is also considered important.
The Gemara elaborates: The exodus from Egypt, as it is written: “When Israel came forth out of Egypt, the house of Jacob from a people of strange language” (Psalms 114:1). And the splitting of the Red Sea, as it is written: “The sea saw it and fled; the Jordan turned backward” (Psalms 114:3). The giving of the Torah, as it is written: “The mountains skipped like rams” (Psalms 114:4), which is similar to the description of the giving of the Torah found elsewhere in the books of the Prophets. The resurrection of the dead, as it is written: “I will walk before the Lord in the lands of the living” (Psalms 116:9), which follows the verse: “For you have delivered my soul from death.” After mentioning death, the psalm describes the resurrection in the lands of the living.
The pangs of the Messiah, as it is written: “Not to us, God, not to us, but to Your name give glory” (Psalms 115:1). And Rabbi Yoḥanan said: The verse “Not to us, God, not to us” and the entire psalm, including the verse “Why should the nations say, where now is their God?” (Psalms 115:2), is referring to the era of the enslavement of the kingdoms and the redemption of the Jewish people from their dominion. Some say that Rabbi Yoḥanan said: The verse “Not to us, God, not to us” is referring to the war of Gog and Magog, the catastrophes and wars that will befall the Jewish people in the end of days from which they will be delivered. 

Both the Bavli and the Yerushalmi say that only the first two chapters of Hallel are Hallel Mitzrayim. All the rest of Hallel speaks of the present and the future. The division of the two sections is exactly in keeping with the order of the Seder, beginning with the celebration of Yetzias Mitzrayim, and ending with our faith in Hashem's presence during Galus and His ultimate return of the Shechina to Eretz Yisrael with Biyas Mashiach. The second section can certainly be recited after Chatzos.

This year, at our lonely sedarim, as we celebrate the Geulas Mitzrayim, let us hopefully and confidently and joyously sing of the Geula Ha'asida.