I'd be quite surprised if they did. After all, those who analyze the classic Beis Hill/Shamai argument (such as R' Reuven Margaliyos in many of his Sefarim) tend to say that Beis Hillel had more flexibile halachic parameters than Beis Shamai (of course, within halachah). Being that Rebbi Tarfon and Rebbi Akiva are being lenient, it doesn't seem to fit the typical pattern. [By the way, I am quite impressed with your knowledge that Rebbi Akiva was somewhat rooted in Beis Shamai (see Toras Chaim in Bava Basra 158b).]

All the best,

Yaakov Montrose