Is it permissible to prolong the glorification (tasbih) and supplication (du'a) in prostration (sujud) and the final tashahhud after the Imam has risen but before he has given the salutation, and then to follow him thereafter?

There is no impediment in what you were doing, occupying yourself with supplication (du'a) and remembrance (dhikr) while the Imam moves from one pillar (rukn) to another, as this is better than remaining silent. This is supported by the fact that if the worshipper (ma'mum) finishes reciting Al-Fatiha and does not hear the Imam's recitation, or if it is a silent prayer (sirriyah) or the third and fourth rak'ahs of a four-rak'ah prayer, it is sunnah for him to recite or supplicate, and recitation is better. He should not remain silent, because there is no silence in prayer except in specific instances, and this is not one of them. Likewise, there is no harm in continuing to supplicate while the Imam is performing the taslim (salutation of peace), and it is permissible to engage in supplication after the Imam has performed the taslim.