megillat esther - How could Haman see Gd's face and live?

Continuing the series:

The Megillah writes:

יד וְהַקָּרֹב אֵלָיו, כַּרְשְׁנָא שֵׁתָר אַדְמָתָא תַרְשִׁישׁ, מֶרֶס מַרְסְנָא, מְמוּכָן--שִׁבְעַת שָׂרֵי פָּרַס וּמָדַי, רֹאֵי פְּנֵי הַמֶּלֶךְ, הַיֹּשְׁבִים רִאשֹׁנָה, בַּמַּלְכוּת.‏

14 and the next unto him was Carshena, Shethar, Admatha, Tarshish, Meres, Marsena, and Memucan, the seven princes of Persia and Media, who saw the king's face, and sat the first in the kingdom:

In the Torah it tells us:

כ וַיֹּאמֶר, לֹא תוּכַל לִרְאֹת אֶת-פָּנָי: כִּי לֹא-יִרְאַנִי הָאָדָם, וָחָי

20 And He said: 'Thou canst not see My face, for man shall not see Me and live.'

Since we are told that every instance of the Word "King" in the megillah* is refering to Gd, how were Carshena, shethar, Admatha, Tarshish, Meres, Marsena and Memucan(aka Haman), able to see G'd face and live? And what "face of Gd", did they see?

And, what did Vashti do against Hashem? Such that Memucan (which the Meforshim say was Haman) could say:

טז וַיֹּאמֶר מומכן (מְמוּכָן), לִפְנֵי הַמֶּלֶךְ וְהַשָּׂרִים, לֹא עַל-הַמֶּלֶךְ לְבַדּוֹ, עָוְתָה וַשְׁתִּי הַמַּלְכָּה: כִּי עַל-כָּל-הַשָּׂרִים, וְעַל-כָּל-הָעַמִּים, אֲשֶׁר, בְּכָל-מְדִינוֹת הַמֶּלֶךְ אֲחַשְׁוֵרוֹשׁ.‏

16 And Memucan answered before the king and the princes: 'Vashti the queen hath not done wrong to the king only, but also to all the princes, and to all the peoples, that are in all the provinces of the king Ahasuerus.

• Thank you @Jake for finding the reference: (my translation)

Gra on Esther (derech remez): ואמרו חכמינו ז"ל במדרש כל מקום שנאמר המלך סתם הוא הקדוש ברוך הוא וכל מקום שנאמר אחשורוש באחשורוש ממש מדבר.

And our sages of blessed memory say, in midrash, all the places that it says "King" alone, this refers to Gd, and all the plaes that it says "Acheshverosh", it is speaking of Acheshverosh only.

Now, I will admit, that when I first heard the idea that every place it says Melech alone it means Gd, that I went and tried to see if it was true. It seemed to me the idea is false, but, if it isn't, I want to understand what these verses are telling us.

Answer

The Gemara (Megillah 12b) sees the names of these seven courtiers as hinting at various aspects of the sacrificial service in the Beis Hamikdash. For example, כרשנא is explained as a portmanteau of כרים (בני) שנה, fat sheep in their first year; שתר, of שתי תורין (two turtledoves); etc. Since coming to the Beis Hamikdash to offer sacrifices is often described as ראיית פנים (e.g., Ex. 23:15,17, 34:20,23; Is. 1:12), then indeed this group can be described as "those who see the King's (Hashem's) face."

(Incidentally, that Memuchan is Haman is not universally accepted. Tosafos there cites a Midrash that identifies him with Daniel.)

See also Ohr Hatorah (by the Tzemach Tzedek of Lubavitch), where he cites several sources that associate "the seven princes... who see the face of the King" with those who serve Hashem in high-level Torah study and prayer.

As for Vashti, she indeed offended not only the earthly king but also the Divine one - as per the well-known explanation (Megillah ibid.) about how she forced Jewish girls to work on Shabbos.