What is the solution for dealing with the intrusive thoughts of changing the intention of prayer during the Takbir, and is it sufficient to disregard them and perform the Takbir even if the worshiper feels the intention has shifted to another prayer for the prayer to be valid?

We advise you to continue striving against your lower self, to proceed with the treatment, and to disregard the whispers. The whispering concerning intention, like other whispers, is resolved by ignoring it. So, if you wish to pray, intend the specific prayer you desire and immediately say the opening "Allahu Akbar" (Takbirat al-Ihram) without hesitation. If Satan whispers to you that you did not intend, do not pay attention to him. It is sufficient for you to bring the prayer to mind in your heart and then say the Takbir, and your prayer will be valid thereby.