Been through almost exactly this with my static caravan a couple of winters back — condensation was absolutely relentless no matter what I tried.
The thing that genuinely shifted it for me was a combination attack rather than one silver bullet. First, I tracked down every cold bridge I could find — in my case it was the steel frame sections that were basically acting as radiators for the outside air. Thermal break tape sounds unglamorous but it made a measurable difference.
Second, and this one surprised me — I was under-ventilating trying to stay warm. Counterintuitive, but a bit of controlled airflow via a small Lunos or similar heat recovery unit stops the moisture-laden air just sitting there doing damage.
What's your current heating setup? In the shepherd's hut I'd suspect a lot depends on whether you're running something that burns — wood burner, diesel — because that's pumping moisture into a very small volume. LPG is the worst offender for this, funnily enough.
Also worth asking: how thick is your insulation, and is it breathable or foil-faced? Foil-faced in a small timber structure can trap moisture between layers if it's not properly sealed, which just migrates to the nearest cold surface.
Curious whether others have found damp-trap solutions like the Meaco units useful in something that compact, or whether they just fight a losing battle without sorting the root cause first.
Would love to see what your build looks like internally — sometimes a photo tells you more than a thousand words on these things.