The news of Mexico's independence would not have come via land route but by merchant ships. Vera Cruz, Mexico was was the largest port i 1821 and traded goods with New Orleans. It to 7 to 14 days to make this voyage.
That meant the news would have traveled up the Mississippi to St. Louis which took 10 to 20 days by steamboat.
Best case...news would have reached st louis by Sept 10th
Worse case...Sept 27th
For TB to be in Lynchburg in December, he would have had to leave st louis i October 31st.
So the news of Mexico's independence would have been well know by the time his parry reached STL.
You are right that the letter/ciphers were written after December 1821 and retold the story of their first trip when they found gold. But since it was written after the Mexico's independence, he most certainly could have used Mexican town in the retelling of the account.