Is it permissible to agree upon a symbolic dowry (mahr) to apply the Sunnah, and then present a large sum as a gift to the wife immediately after the marriage contract (aqd)? And is this considered a deception against the religion?

Facilitating dowries is a legitimate Islamic requirement and a prophetic guidance due to the great religious benefits that accrue from it. Islamic law has not specified a particular amount for the dowry; there is no minimum or maximum limit for it. What you are doing by agreement with your wife and her family is not forbidden, but it does not achieve the reduction of the dowry, because it will be the total of what you named in the contract and what you will pay her afterwards. If the dowry is within the customary range for women of her standing, there is no reprehensibility in it, and it does not fall under the purview of religiously disliked extravagance.