Yes, you are correct but 'gotten' seems to be far more widely-used in America (as the past-participle of 'get') than it does in British English - with the exception of the cliche 'ill-gotten gains'. I'm a 'Brit' so for some reason 'gotten' just sounds weird to me. You are also correct that 'snuck' just kind of 'sneeked' into American English, yet for some reason it actually sounds 'right' (if you know what I mean)

Back to the main point for a moment and to those lovely people at New Concept English
Yesterday I had a grade 7 esl student ask me to help her with a homework question

Enter the correct phrase - a) Will you please b) Please will you

"...................open the window?"

Of course, under the Chinese English teaching system, only ONE is correct..............ridiculous !