Is it permissible to prolong the prostration (sujood) without prolonging the other pillars of prayer, and how can one reconcile extensive supplication during prostration with the hadith about proportionality in prayer?

What is established from the Prophet's guidance (peace and blessings be upon him) is that his prayers were balanced and moderate. If he prolonged the standing, he would prolong the bowing and prostration. Anas (may Allah be pleased with him) described his prayer as the lightest yet most complete, due to its moderation and proportion. This ruling applies to the Imam. As for the one praying alone, he may prolong prostration with supplication as much as he wishes.