Pesach and Sukkot: Inconsistent Occurrences, Add your Opinion!

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And now, let's start with the dilemmas.

(א) וַיִּשְׁלַח יְחִזְקִיָּהוּ עַל כָּל יִשְׂרָאֵל וִיהוּדָה וְגַם אִגְּרוֹת כָּתַב עַל אֶפְרַיִם וּמְנַשֶּׁה לָבוֹא לְבֵית יְהוָה בִּירוּשָׁלָ‍ִם לַעֲשׂוֹת פֶּסַח לַיהוָה אֱלֹהֵי יִשְׂרָאֵל... (כו) וַתְּהִי שִׂמְחָה גְדוֹלָה בִּירוּשָׁלָ‍ִם כִּי מִימֵי שְׁלֹמֹה בֶן דָּוִיד מֶלֶךְ יִשְׂרָאֵל לֹא כָזֹאת בִּירוּשָׁלָ‍ִם.

(1) And Hezekiah sent to all Israel and Judah, and wrote letters also to Ephraim and Manasseh, that they should come to the house of the LORD at Jerusalem, to keep the passover unto the LORD, the God of Israel... (26) So there was great joy in Jerusalem; for since the time of Solomon the son of David king of Israel there was not the like in Jerusalem.

Shlomo's Feast
(א) אָז יַקְהֵל שְׁלֹמֹה אֶת זִקְנֵי יִשְׂרָאֵל אֶת כָּל רָאשֵׁי הַמַּטּוֹת נְשִׂיאֵי הָאָבוֹת לִבְנֵי יִשְׂרָאֵל אֶל הַמֶּלֶךְ שְׁלֹמֹה יְרוּשָׁלָ‍ִם לְהַעֲלוֹת אֶת אֲרוֹן בְּרִית יְהוָה מֵעִיר דָּוִד הִיא צִיּוֹן. (ב) וַיִּקָּהֲלוּ אֶל הַמֶּלֶךְ שְׁלֹמֹה כָּל אִישׁ יִשְׂרָאֵל בְּיֶרַח הָאֵתָנִים בֶּחָג הוּא הַחֹדֶשׁ הַשְּׁבִיעִי.
(1) Then Solomon assembled the elders of Israel, and all the heads of the tribes, the princes of the fathers’houses of the children of Israel, unto king Solomon in Jerusalem, to bring up the ark of the covenant of the LORD out of the city of David, which is Zion. (2) And all the men of Israel assembled themselves unto king Solomon at the feast, in the month Ethanim, which is the seventh month.

(כא) וַיְצַו הַמֶּלֶךְ אֶת כָּל הָעָם לֵאמֹר עֲשׂוּ פֶסַח לַיהוָה אֱלֹהֵיכֶם כַּכָּתוּב עַל סֵפֶר הַבְּרִית הַזֶּה. (כב) כִּי לֹא נַעֲשָׂה כַּפֶּסַח הַזֶּה מִימֵי הַשֹּׁפְטִים אֲשֶׁר שָׁפְטוּ אֶת יִשְׂרָאֵל וְכֹל יְמֵי מַלְכֵי יִשְׂרָאֵל וּמַלְכֵי יְהוּדָה. (כג) כִּי אִם בִּשְׁמֹנֶה עֶשְׂרֵה שָׁנָה לַמֶּלֶךְ יֹאשִׁיָּהוּ נַעֲשָׂה הַפֶּסַח הַזֶּה לַיהוָה בִּירוּשָׁלָ‍ִם.

(21) And the king commanded all the people, saying: ‘Keep the passover unto the LORD your God, as it is written in this book of the covenant.’ (22) For there was not kept such a passover from the days of the judges that judged Israel, nor in all the days of the kings of Israel, nor of the kings of Judah; (23) but in the eighteenth year of king Josiah was this passover kept to the LORD in Jerusalem.

Why is Melachim skipping over Chizkiyah's Pesach?

(יז) וַיַּעֲשׂוּ כָל הַקָּהָל הַשָּׁבִים מִן הַשְּׁבִי סֻכּוֹת וַיֵּשְׁבוּ בַסֻּכּוֹת כִּי לֹא עָשׂוּ מִימֵי יֵשׁוּעַ בִּן נוּן כֵּן בְּנֵי יִשְׂרָאֵל עַד הַיּוֹם הַהוּא וַתְּהִי שִׂמְחָה גְּדוֹלָה מְאֹד. (יח) וַיִּקְרָא בְּסֵפֶר תּוֹרַת הָאֱלֹהִים יוֹם בְּיוֹם מִן הַיּוֹם הָרִאשׁוֹן עַד הַיּוֹם הָאַחֲרוֹן וַיַּעֲשׂוּ חָג שִׁבְעַת יָמִים וּבַיּוֹם הַשְּׁמִינִי עֲצֶרֶת כַּמִּשְׁפָּט.

(17) And all the congregation of them that were come back out of the captivity made booths, and dwelt in the booths; for since the days of Joshua the son of Nun unto that day had not the children of Israel done so. And there was very great gladness. (18) Also day by day, from the first day unto the last day, he read in the book of the Law of God. And they kept the feast seven days;

And why is Nechemya skipping over Shlomo's Sukkot?

This is my guess.

(ב) וַיִּוָּעַץ הַמֶּלֶךְ וְשָׂרָיו וְכָל הַקָּהָל בִּירוּשָׁלָ‍ִם לַעֲשׂוֹת הַפֶּסַח בַּחֹדֶשׁ הַשֵּׁנִי. (ג) כִּי לֹא יָכְלוּ לַעֲשֹׂתוֹ בָּעֵת הַהִיא כִּי הַכֹּהֲנִים לֹא הִתְקַדְּשׁוּ לְמַדַּי וְהָעָם לֹא נֶאֶסְפוּ לִירוּשָׁלָ‍ִם.

(2) For the king had taken counsel, and his princes, and all the congregation in Jerusalem, to keep the passover in the second month. (3) For they could not keep it at that time, because the priests had not sanctified themselves in sufficient number, neither had the people gathered themselves together to Jerusalem.

Legal justification for this to follow.

(י) דַּבֵּר אֶל בְּנֵי יִשְׂרָאֵל לֵאמֹר אִישׁ אִישׁ כִּי יִהְיֶה טָמֵא לָנֶפֶשׁ אוֹ בְדֶרֶךְ רְחֹקָה לָכֶם אוֹ לְדֹרֹתֵיכֶם וְעָשָׂה פֶסַח לַיהוָה. (יא) בַּחֹדֶשׁ הַשֵּׁנִי בְּאַרְבָּעָה עָשָׂר יוֹם בֵּין הָעַרְבַּיִם יַעֲשׂוּ אֹתוֹ עַל מַצּוֹת וּמְרֹרִים יֹאכְלֻהוּ.

(10) ’Speak unto the children of Israel, saying: If any man of you or of your generations shall be unclean by reason of a dead body, or be in a journey afar off, yet he shall keep the passover unto the LORD; (11) in the second month on the fourteenth day at dusk they shall keep it; they shall eat it with unleavened bread and bitter herbs;

Chizkiyahu kept Pesach Sheni, while Yoshiyahu kept real Pesach.

(יז) וַיַּעֲשׂוּ כָל הַקָּהָל הַשָּׁבִים מִן הַשְּׁבִי סֻכּוֹת וַיֵּשְׁבוּ בַסֻּכּוֹת כִּי לֹא עָשׂוּ מִימֵי יֵשׁוּעַ בִּן נוּן כֵּן בְּנֵי יִשְׂרָאֵל עַד הַיּוֹם הַהוּא וַתְּהִי שִׂמְחָה גְּדוֹלָה מְאֹד. (יח) וַיִּקְרָא בְּסֵפֶר תּוֹרַת הָאֱלֹהִים יוֹם בְּיוֹם מִן הַיּוֹם הָרִאשׁוֹן עַד הַיּוֹם הָאַחֲרוֹן וַיַּעֲשׂוּ חָג שִׁבְעַת יָמִים וּבַיּוֹם הַשְּׁמִינִי עֲצֶרֶת כַּמִּשְׁפָּט.

(17) And all the congregation of them that were come back out of the captivity made booths, and dwelt in the booths; for since the days of Joshua the son of Nun unto that day had not the children of Israel done so. And there was very great gladness. (18) Also day by day, from the first day unto the last day, he read in the book of the Law of God. And they kept the feast seven days;

Throughout Melachim, Chapter 8 (which is too big for addition here but can be viewed at www.sefaria.org/I_Kings.8), there is no mention of building Sukkot. This could solve the second problem.

Have any other ideas? Feel free to post them here. Thanks for reading!