Should the congregant bow with the Imam in the last two rak'ahs if he joins them during this part of the prayer, or should he wait and recite three verses, considering it his first rak'ah? And is Tasbeeh not obligatory during the prostration of forgetfulness according to the Hanafis, by analogy with its non-obligation in the prostration between the two prostrations during prayer?

The Hanafi school of thought holds that the follower (ma'mum) should not recite behind the Imam, neither in audible nor in silent prayers. Rather, it is obligatory for him to listen attentively, even if he does not hear the Imam's recitation, based on the Almighty's saying: {And when the Qur’an is recited, listen to it and pay attention.} So, if the follower adheres to the Hanafi school, he should bow immediately, following his Imam, without reciting.

As for glorification (tasbih) in the prostration of forgetfulness (sujud as-sahw), it is a sunnah according to the Hanafis, and it is sunnah for the worshipper to say: "Glorified be He who neither sleeps nor forgets" along with the usual prostration glorification.