Yoma 77a - aiyeif and lack of sleep

The gemara is trying to figure out one of the "five inuyim" (five types of fasting required on Yom Kippur) from a verse with the word עיף. Now עיף is usually translated, "tired". The gemara considers three possibilities: no shoes, no drinking, and (the right answer) no washing.
I am just wondering why it did not consider the obvious answer: that "tired" means no sleeping. Maybe we are not allowed to sleep on Yom Kippur - that seems like a good עינוי! And of course it is something that many have tried to do, including the kohen gadol in the Mishnah (though the poskim say that it isn't a good idea because you'll sleep through the davening the next day).

Am I mistaken about the meaning of עיף? By Esav it seems to have meant, wiped out and starving. The Concordance lists three synonyms: עיף, יגיע, and נלאה. From the examples, נלאה seems to mean "fed up", "wearied and sick of". יגע seems to mean "tired from hard work", like יגיע כפיך, and ושם ינוחו יגיעי כח. And עיף seems to mean physically wiped out. But I guess none of them means, sleepy?

The word that usually seems to mean "sleepy" is נרדם. Interestingly, most times it appears to give an impression of something that was done to the person externally, such as with Adam Harishon: Hashem cast a deep sleep (תרדמה) on the man... Or with Avram in the Bris Bein Hab'sarim: "The sun had set, and a תרדמה fell on Avram..." Even by Sisera, where I thought sure that he would be sleepy, it just says that he was very thirsty. Then, after Yael drove a peg into his temple, it says, וַתִּצְנַח בָּאָרֶץ וְהוּא־נִרְדַּם וַיָּעַף וַיָּמֹת - he sank down on the ground, became unconscious and tired (?) and died (?!)