As in sentences like "I'm satisfied that you did your best" and "I'm satisfied that it contains no gluten". Do those not work in American or other international English?

According to google ngrams the frequency of 'satisfied that' is 0.00026% in British English and 0.00012% in American English. So only a factor of 2 difference. Interestingly the peak of American usage was in the 1860s (~0.001%), followed by a slow decline, but in Britain there was a small peak around 1920 (~0.00127%), then a higher peak in the 1940s (~0.002%), followed by a rapid decline to the present day.

No, that's the definition that does track perfectly in American English: where it can be substituted by "pleased."

But those sentences are also perfectly meaningful assuming the other sense of "satisfied", which may be what GP meant. Ie. "I am convinced that you did your best" and "I am convinced that it contains no gluten".

Oh, I definitely agree that those example exist on the fuzzy line, but the question was whether they didn't read to Americans.

The more I think about it, the harder the actual barrier between "pleased" and "convinced" is hard to draw.

It's not that hard to draw it: 'I am satisfied that this man is the one who killed my dog'. Whether you are convinced that this is the man, or whether you are pleased that this particular man killed your dog are clearly different senses.

But would you not be pleased to be certain who killed your dog? It's not a 1:1 concept mapping, but the conceptual space is close enough that the semantic drift of "satisfied" is completely understandable.

I am satisfied that I am satisfied that this is the man who killed my dog ;)