I'm just going by your idea of needing to be self-sustaining for several weeks or possibly months.

The Millbank only filters particulates but it is much better than a bandanna at it and allows more volume. You can also use one (properly sized and perhaps modified) as a carrier/protection for a solar shower or one gallon ziplock freezer bag(s) for transporting water (to a more secure or secluded location if needed) before purifying it. BTW a solar shower may not fit a "minimalist" approach but believe me, after a few weeks of "[censored]'s baths" or bathing in lakes, rivers or streams, even a luke warm shower is a great morale booster and a hot shower is better than sex (almost).

Another dietary fat idea would be several small cans of clarified butter. It should usually be refrigerated after opening but it should be safe if kept in a evaporation cooler (like a canteen cover kept damp).