I could have just said this...but man, what a short video!
I don't think the dietary laws, and circumcision and whatnot really fall into the category of "good works". I see them more as just complying with the laws God set down in the original covenant. Until Paul came along, nobody doubted that the original rules still applied. And as rules, they're more for demonstrating that you recognize God as Lord, and seek to please Him.
As you say, Galations was written before any of the four gospels, so it seems to me that if Paul (who never met Jesus) was preaching something completely different than Jesus's brother (who spent his whole life talking with Jesus), James was probably more in line with how Jesus viewed the Levitical laws than Paul was.
I think Paul was so intent on attracting non-Jews to his new religion, that he found ways to convince himself that the rules didn't apply anymore. Too hard to get the Greeks to fully sign up if you tell them they have to get circumcised first. And once you throw out one of the rules, you might as well throw them all out. Just tell the people that there are no more rules anymore and that faith is the only important thing.