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Try Yandex Translator, it is much better suited for Russian translations.

It almost looks promising, but at the end of the day, use of their API still requires a monthly fee.  I would need a solution that relies on the user instead of me I think.  If it's possible to let others sign up for an API key and input it into the game to translate, that may work, though I would need to be very careful that it doesn't break terms of service or cause legal troubles.