Your instincts seem pretty good already. I don't know about "best", which is subjective, but your basic options are one or more of:

1. Make the incoming light less intense and/or more diffuse. E.g.:
   1. Use a scrim as mentioned in the comment above.
   2. Film in existing or created partial shade. E.g. in a barn with open doors, under a tree, etc. (Though you ruled out artificial structures.)
2. Enhance or create lower-angle light, to counteract the shadows. E.g.
   1. Carry a fill light, which could qualify as "basic" equipment depending on your situation and requirements.
   2. Carry or borrow a very light-colored and/or reflective blanket, sheet, paper, etc. - to place below the subject but out of camera view. This alone can be pretty effective. Your mylar blanket would work, but depending on how irregular the surface is, might cast unacceptable bright splotches randomly. A tyvek blanket, or nylon sheet, can be great for filling in light under hats.
3. You said this wasn't an option, but just to reiterate one of the best natural options, film when the sun is low on the horizon, and/or just after sunset or before sunrise. (Obviously at high and dry mountain elevations, such soft light may not last very long.) Do the farmers start work very early?

You've probably considered these very options and are more asking if there's a better "best-practice". But I think your existing instincts are on the "right" track.