akeidas Yitzchak - all a big misunderstanding?

A hypothetical question: If I think that there is a mitzvah to walk barefoot to shul every day, and I fulfill that mitzvah with great mesirus nefesh, with blisters on my feet in the summer, and even at the cost of getting frostbite in the winter, do I get schar for a kiyum mitzvah?

This should not require much thought to answer.  How can I get schar for a mitzvah that's not a mitzvah?  Yes, there is schar for good intentions: אפילו חשב אדם לעשות מצוה, ונאנס ולא עשאה, מעלה עליו הכתוב כאילו עשאה (Kid 40a), but that's where the good intentions were to do a mitzvah.  In this case, there is no mitzvah!  

Seems like an obvious point, but it also seems to fly in the face of our tefilos and our understanding of this week's parsha.  We call upon Hashem to remember the zechus of akeidas Yitzchak.  We view akeidas Yitzchak as the greatest act of mesirus nefesh and ahavas Hashem; it was the greatest test Avraham was called upon to pass, and which he did with flying colors.  Yet Rashi comments on G-d's command וְהַעֲלֵהוּ שָׁם לְעֹלָה עַל אַחַד הֶהָרִים אֲשֶׁר אֹמַר אֵלֶיך that:

 לא אמר לו: שחטהו, לפי שלא היה חפץ הקב״ה לשחטו, אלא יעלהו להר לעשותו עולה, ומשהעלהו, אמר לו: הורידהו

G-d told Avraham to bring Yitzchak up to the mountain, but not to actually sacrifice him. There was never such a mitzvah!  

Does this mean that Avraham chopping wood, taking a knife, preparing to sacrifice his son, was all a big mistake and misunderstanding?  Did Avraham misinterpret the dvar Hashem?  

If there was never such a mitzvah, why do invoke the schar Avraham's deed forever after?  It's not schar for just carrying Yitzchak up and down the mountain, but schar for the willingness to sacrifice Yitzchak that we are asking Hashem to remember.  If that was never a mitzvah, why should it be worth any more reward any more than my walking to shul barefoot?  

R' Shmuel Birnbaum (in Tiferes Shmuel on the parsha) answers this question with a yesod developed by the Ketzos in his introduction.  The gemara (BM 86a) writes that there was a machlokes in heaven about a din in hil negaim:

 קָא מִיפַּלְגִי בִּמְתִיבְתָּא דִרְקִיעָא: אִם בַּהֶרֶת קוֹדֶמֶת לְשֵׂעָר לָבָן – טָמֵא, וְאִם שֵׂעָר לָבָן קוֹדֵם לַבַּהֶרֶת – טָהוֹר.

סָפֵק – הַקָּדוֹשׁ בָּרוּךְ הוּא אוֹמֵר: טָהוֹר, וְכוּלְּהוּ מְתִיבְתָּא דִרְקִיעָא אָמְרִי: טָמֵא. וְאָמְרִי: מַאן נוֹכַח? נוֹכַח רַבָּה בַּר נַחְמָנִי. דְּאָמַר רַבָּה בַּר נַחְמָנִי: אֲנִי יָחִיד בִּנְגָעִים, אֲנִי יָחִיד בְּאֹהָלוֹת

כִּי הֲוָה קָא נָיְחָא נַפְשֵׁיהּ, אֲמַר: טָהוֹר, טָהוֹר. יָצָאת בַּת קוֹל וְאָמְרָה: אַשְׁרֶיךָ רַבָּה בַּר נַחְמָנִי שֶׁגּוּפְךָ טָהוֹר, וְיָצָאתָה נִשְׁמָתְךָ בְּטָהוֹר

How could Rabbah bar Nachmaini resolve a machlokes between G-d himself and the mesivra d'rekiya!?  Isn't it obvious that G-d knows the right answer?

The Ketzos quotes the Derashos haRan as explaining that built into the Torah is the allowance for different possible interpretations.  "Eilu v'eilu divrei Elokim chaim."  In an absolute sense there is no one "right" answer.  So how do we figure our what to do?  The Torah resolves the problem with the principle of "lo ba'shamayim hi" - the final arbiter of what is "correct" is whatever the chachmei ha'dor think is correct.  It's in our hands to determine the "right" answer.  Therefore, the heavens had to turn to Rabbah bar Nachmeini, the posek ha'dor in hil negaim, to determine exactly what the psak should be.  It's not what's "right" in heaven that matters, but rather what we think is "right" on earth.

The Midrash (B"R 8:5) writes that there was a debate among the angels as to whether or not it was worth it to create man:

אָמַר רַבִּי סִימוֹן, בְּשָׁעָה שֶׁבָּא הַקָּדוֹשׁ בָּרוּךְ הוּא לִבְרֹאת אֶת אָדָם הָרִאשׁוֹן, נַעֲשׂוּ מַלְאֲכֵי הַשָּׁרֵת כִּתִּים כִּתִּים, וַחֲבוּרוֹת חֲבוּרוֹת, מֵהֶם אוֹמְרִים אַל יִבָּרֵא, וּמֵהֶם אוֹמְרִים יִבָּרֵא, הֲדָא הוּא דִכְתִיב (תהלים פה, יא): חֶסֶד וֶאֱמֶת נִפְגָּשׁוּ צֶדֶק וְשָׁלוֹם נָשָׁקוּ. חֶסֶד אוֹמֵר יִבָּרֵא, שֶׁהוּא גּוֹמֵל חֲסָדִים. וֶאֱמֶת אוֹמֵר אַל יִבָּרֵא, שֶׁכֻּלּוֹ שְׁקָרִים. צֶדֶק אוֹמֵר יִבָּרֵא, שֶׁהוּא עוֹשֶׂה צְדָקוֹת. שָׁלוֹם אוֹמֵר אַל יִבָּרֵא, דְּכוּלֵיהּ קְטָטָה. מֶה עָשָׂה הַקָּדוֹשׁ בָּרוּךְ הוּא נָטַל אֱמֶת וְהִשְׁלִיכוֹ לָאָרֶץ, הֲדָא הוּא דִכְתִיב (דניאל ח, יב): וְתַשְׁלֵךְ אֱמֶת אַרְצָה,

What does it mean that G-d threw emes down to earth?  How does silencing truth's voice, removing his platform, address the issue raised?  

R' Yaakov Kaminetzki (in Emes l'Yaakov) explains that there are two different levels or standards of truth: there is absolute truth, and then there is the relative truth that we humans are used to dealing with.  When you sing "kallah na'ah v'chasudah" at a wedding (Kesubos 17), it doesn't matter whether or not the kallah is really beautiful as measured on some absolute scale of beauty.  All that matters is that in her chosson's eyes she is beautiful.  As far as he is concerned, relative to his frame of reference, it's the truth.  When the Midrash says that Hashem kicked the midah of emes down to earth, it doesn't mean that Hashem chose to disregard truth.  What it means is that the standard of truth for mankind is not absolute truth as it exists in heaven, but is relative truth as it exists for us on earth.  

"Lo ba'shamayim hi" means the same is true of halacha.  The "right" answer is the one that appears correct to us, not what is "right" in some absolute sense.

R' Shmuel Birnbaum is mechadesh that the same principle applies to nevuah.  What the prophet sees or hears is subject to his interpretation, and that is what determines the meaning of the nevuah.  When Avraham was commanded הַעֲלֵהוּ שָׁם לְעֹלָה, since Avraham interpreted that to mean that Hashem was asking him to sacrifice Yitzchak, the act of literal sacrifice became a mitzvah.  It doesn't matter in an absolute sense what Hashem meant or didn't mean, because that is not the standard by which we determine what halacha or nevuah means.  The standard of truth is our perception (by "our" I mean the chachmei ha'mesorah or the navi) of what is meant. 

We say in the bracha before the haftarah אֲשֶׁר בָּחַר בִּנְבִיאִים טוֹבִים, וְרָצָה בְדִבְרֵיהֶם הַנֶאֱמָרִים בֶּאֱמֶת.  R'SB explains that when we say the words הַנֶאֱמָרִים בֶּאֱמֶת, we are not thanking Hashem for giving us prophets that don't c"v lie -- that should go without saying.  What we are affirming in our bracha is this principle that the navi's interpretation of the dvar Hashem -- his perception of what Hashem meant -- is true, נֶאֱמָרִים בֶּאֱמֶת, because that is the only truth that is relevant and that counts.