Rabbeinu Tam (who technically allows her to eat Terumah) is talking about a Shomeres L'bias Heter (at least MedRabanan (see Rambam Hil. Terumah end of Chap. 7)), but in the case of the KG she is Shomeres L'bias Issur Shel Torah and does not eat Terumah (Rambam ibid 7:21Rambam ibid 7:21). We do not find that RT holds that Zeikas Yovom that is Ossur Min Hatorah is considered his wife and eats Terumah. Also see Mishna and Rashi Yevomos 56bYevomos 56b.
In general, Shulchan Aruch Orach Chayim 339:4 it says Chalitzah can not be done on Shabbos, and in 524:1 it says it can not be done on Yom Tov. Also keep in mind that he has to wear a shoe to do Chalitzah and the type of shoe for Chalitza is one that can not be worn on Yom Kippur (see Yevomos 202b).