There is a simple answer based on the last pasuk quoted-- "And Haman was filled with hate."
Meaning, by the time he got to Cheimah, he was full, and could no longer accept any more angel-influences.
Due to the double meaning of ‘Af’ (Anger/Nose), many think that Haman did not have a nose, or at least had a detachable nose. This misconception was part of Hashem’s plan (Devarim 32:26):
אמרתי אפאיהם אשביתה מאנוש זכרם
I (G-d) said regarding their noses, I will erase their remembrance
from man (The plural 'their' is referring to Haman and his sons; this trait of
forgotten noses was seemingly hereditary).
The real situation of Haman's nose is as follows.
Haman shows up Shmot 16, and it says he was measured by, and equal to, the Omer, which was 1/10 of an Eifah (Shmot 16:36) And now for the math.
An Eifah is 3 Se'ot, and so Haman was .3 of a Se'ah (a Se'ah is a measure of volume).
The Gemara tells us:
אמה על אמה ברום שלש אמות ושיערו חכמים שיעור מי מקוה ארבעים סאה
(A mikvah must be) One square Amah, with a depth of three Amot; and the Chachamim measured the minimum measure of the Mikvah water to be 40 se'ah (Pesachim 109b).
Assuming an Amah is ~20 inches, 8000*3 cubic in.= 24,000 cubic in.= 40 se'ah. Divide by 40 on both sides, and one Se'ah is equal to 600 cubic inches. Multiply by 3/10, and one Omer is equal to 180 cubic inches, or a cube with a side of approximately 5.65 inches.
Now, the same Gemara used above for the conversion of Amot to Se'ot states that an average human is 3 Amot^3; this yields a rectangle of 60*20*20 in.
Thus, Haman, was a midget, and his nose was merely minuscule, not detachable/non-existent.