Some commentaries say the simple meaning of the Gemara is that Sarah checked for lice.

(a) The Maharsha (DH Ashkechei) writes that when the Gemara says that Avraham "slept," it means that the Tzadikim are called alive even in their deaths (see Berachos, end of 18a). For the Tzadikim, dying is merely like sleeping, as we say in the Shemoneh Esreh, "And He upholds his faith to those who sleep in the dust."

The Maharsha writes that it is Derech Eretz to examine the heads of sleeping people. He cites a source for this from Bava Metzia (84b), where the wife of Rebbi Eliezer b'Rebbi Shimon looked at her deceased husband's hair. (The Gemara there relates that Rebbi Eliezer's body remained perfectly intact after his death for 22 years.) The Menoras ha'Me'or (ch. 18, section Lashon ha'Ra, page 356 in the Bar Ilan Responsa Project) writes that this means that she used to comb his hair. According to this, the Maharsha means that the simple interpretation is that Sarah also checked Avraham's hair.

(b) See also the Nimukei Yosef on the Gemara here (31a of the pages of the Rif, just before the Mishnah), who writes that since the Gemara says that there is no Yetzer ha'Ra in the World to Come, in this world -- where the Yetzer ha'Ra prevails -- it is not appropriate or modest to carry out such practices in front of others, even with one's own wife.

(c) This teaching is in fact recorded as the Halachah. The Rema (EH 21:5) writes that some say that one should not practice in front of others matters of affection with one's wife, such as checking the head for lice. The source of this Halachah is the abovementioned Nimukei Yosef. It is clear that these commentaries understood according to the simple meaning that Sarah checked Avraham's head for lice.

(d) See also Derishah (EH 21:2) who cites Teshuvos ha'Rashba (1:1188) who also explains that Sarah was checking Avraham's hair for Kinim.

(e) However, after having cited all of these sources, it still must be noted that there is clearly something deeper behind the Gemara's account, as the sources you have cited also indicate. At this stage it appears to me that we still require the explanation of the Meshech Chochmah and Rav Yakov Emden to reveal to us what the Gemara really means. There was a checking on the part of Sarah, but the inner secret of this was to check Avraham Avinu's great spiritual purity.

Kol tuv,

Dovid Bloom