passover - Why were the Bechorim punished?

Avraham Avinu says in Bereishit 18:25:

חָלִ֨לָה לְּךָ֜ מֵעֲשֹׂ֣ת ׀ כַּדָּבָ֣ר הַזֶּ֗ה לְהָמִ֤ית צַדִּיק֙ עִם־רָשָׁ֔ע וְהָיָ֥ה כַצַּדִּ֖יק כָּרָשָׁ֑ע חָלִ֣לָה לָּ֔ךְ הֲשֹׁפֵט֙ כָּל־הָאָ֔רֶץ לֹ֥א יַעֲשֶׂ֖ה מִשְׁפָּֽט׃

That be far from Thee to do after this manner, to slay the righteous with the wicked, that so the righteous should be as the wicked; that be far from Thee; shall not the judge of all the earth do justly?’

However, with regards to Makkat Bechorot we are taught (Shmot 12:29-30):

וַיְהִ֣י ׀ בַּחֲצִ֣י הַלַּ֗יְלָה וַֽיהוָה֮ הִכָּ֣ה כָל־בְּכוֹר֮ בְּאֶ֣רֶץ מִצְרַיִם֒ מִבְּכֹ֤ר פַּרְעֹה֙ הַיֹּשֵׁ֣ב עַל־כִּסְא֔וֹ עַ֚ד בְּכ֣וֹר הַשְּׁבִ֔י אֲשֶׁ֖ר בְּבֵ֣ית הַבּ֑וֹר וְכֹ֖ל בְּכ֥וֹר בְּהֵמָֽה׃ וַיָּ֨קָם פַּרְעֹ֜ה לַ֗יְלָה ה֤וּא וְכָל־עֲבָדָיו֙ וְכָל־מִצְרַ֔יִם וַתְּהִ֛י צְעָקָ֥ה גְדֹלָ֖ה בְּמִצְרָ֑יִם כִּֽי־אֵ֣ין בַּ֔יִת אֲשֶׁ֥ר אֵֽין־שָׁ֖ם מֵֽת׃

And it came to pass at midnight, that the LORD smote all the firstborn in the land of Egypt, from the first-born of Pharaoh that sat on his throne unto the first-born of the captive that was in the dungeon; and all the first-born of cattle. And Pharaoh rose up in the night, he, and all his servants, and all the Egyptians; and there was a great cry in Egypt; for there was not a house where there was not one dead.

This begs the question: Were all of the Egyptian firstborn evildoers?

And if the answer is yes, a follow-up: What was unique about the firstborn that only they were killed, whereas all the other evildoers lived?

While this question-and-answer deals with part of the issue, it:

a) Does not give definitive proof that no Egyptian firstborn was innocent.

b) Leaves our second question undealt with (albeit asked by DanF); and surely, middah k'neged middah is no excuse for missing the target!