Supercaps work great. The only drawbacks are a) slightly higher cost, and b) they take some time to first charge up before they can provide backup power. Whatever resistance is in the path of the cap (including internal self-resistance) forms a time constant that can be non-negligible before the cap is fully charged.
Also, in computing your 6.6 days be sure to take into account capacitor self-discharge. See this Panasonic app note for example:
http://industrial.panasonic.com/www-data/pdf/ABC0000/ABC0000TE5.pdf
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The Rugged Audio Shield: Line In, Mic In, Headphone Out, microSD socket, potentiometer, play/record WAV files