A number of friends in Har Nof suggested the following answers:

(a) Rav Nachum Borovsky pointed out that the Rashba and Ritva write (citing Rav Hai) that there is not actually a prohibition to call others "Avos." It is just "a matter of honor," i.e. the only ones deserving of being called the fathers of the nation are the 3 Avos. The Rashba and Ritva also cite the Ra'avad, who explains the Gemara to mean that there is no obligation to mention more than the 3 Avos in prayer.

(b) Rav Mordechai Rabin (Rabinowitz) explained that the prohibition of the Gemara may apply specifically to the Shevatim, and not to others such as Moshe and Aharon etc. Rashi (DH Ela l'Shelosha) indeed says, "[Avos refers to] only Avraham Yitzchak and Yakov, meaning to exclude the Shevatim ."

(c) Perhaps the word "fathers" in the Mi she'Berach prayer only refers to the first three: Avraham Yitzchak and Yakov. (M. Kornfeld) Proof to this can be brought from the fact that the other Mi she'Berach's (for Aliyos, Yoledes, etc., except for the one for the sick) only include the first three, Avraham Yitzchak and Yakov. When praying for the sick we want to arouse all the Zechuyos of our anscestors, so we mention the others - but we still say "Avoseinu," referring to the first three (Y. Shaw)

(See also Insights to Sotah 32b.)