Handling SQL updates for production deployments
I am not sure if you still need an answer, but I had the same problem with managing and deploying schema changes. Sqitch was the first thing I tried to mechanize migrations, but I did not really like it.

Just as you described, we have separate .sql files with CREATE TABLE and other instructions reflecting our database schema. We created simple tool to generate SQL patches when schema changes. Take a look at it: https://github.com/condograde/sqlibrist. There is detailed tutorial, how to use it.