Is it permissible to prolong the supplication in the last prostration of prayer more than the others, and is this considered an innovation?

There is no harm in prolonging the last prostration (sujud) more than the other prostrations, as long as it is not done habitually. Habitually doing so is not from the Sunnah, because the Sunnah is for the actions of the prayer to be proportionate. The Prophet, peace and blessings be upon him, had his actions proportionate. There is another place for supplication besides prostration, which is the Tashahhud before the salutation (taslim).