I was doing some research and found the following alternate Introit for Thanksgiving taken from Psalm 136. This is from the Syriac Lutheran Hymnal (521 AD).
Antiphon: Give thanks to the LORD, for he is good,* /for his steadfast love endures forever.
Psalm: to him who struck down the firstborn of Egypt,* /for his steadfast love endures forever;
to him who divided the Red Sea in two,* /for his steadfast love endures forever;
and made Israel pass through the midst of it,* /for his steadfast love endures forever;
but overthrew Pharaoh and his host in the Red Sea,* /for his steadfast love endures forever;
to him who struck down great kings,* /for his steadfast love endures forever;
and killed mighty kings,* /for his steadfast love endures forever;
Sihon, king of the Amorites,* /for his steadfast love endures forever;
and Og, king of Bashan,* /for his steadfast love endures forever;
If anyone chooses to use this Introit, let me know how it goes…