Is my prayer valid if I stand up to complete the prayer before the Imam has fully completed the Taslim? And do I have to perform the prostration of forgetfulness (sujud al-sahw) if I make a mistake in the wording of the Taslim, then immediately correct it while my head is still turned?

Standing up to make up missed prayers after the Imam's first salutation: - Maliki and Hanbali schools: The prayer becomes invalid if the latecomer stands up before the Imam completes the second salutation, unless the latecomer returns to stand after the Imam's second salutation, in which case their prayer turns into a supererogatory one. - Shafi'i school: It is permissible to stand up after the Imam's first salutation because he has exited the prayer with it. However, it is recommended for the latecomer not to stand up until the Imam has finished both salutations. - The view of the majority is stronger, thus the prayer of one who stands up after the Imam's first salutation is valid. - It is recommended to be cautious and stand up after the Imam's second salutation.

What you mentioned about your tongue slipping and your error in uttering the salutation incurs no blame upon you, Allah willing, especially since you corrected it.