Is it permissible to gift two copies of the Quran with the intention that the reward for reading the first be for living and deceased Muslims, and the reward for reading the second be for the giver and his family?

Donating Qurans to those in need is a charitable act and a means of drawing closer to Allah if the intention is pure. The wording is not what matters; what matters is the intention. There is no requirement to mention a specific formula. It is permissible to dedicate a Quran as a waqf (endowment) and gift its reward to the deceased or the living, and this is considered an ongoing charity (Sadaqah (definition) Jariyah).