I had to look up the motivation for their beliefs, and now I know a touch more about the Amish.
It's not about avoiding technology, it's about avoiding undesired influences on their culture.
As such, I think that a non-violent (they're a pacifist order) but entirely crippling tool to anyone with a dependence on technology would be perfectly acceptable.
Many orders accept batteries but not connection to the power grid. I have to believe that would extend to capacitor banks, particularly since capacitors predate when the Amish started to eschew technology and not just outsiders.
So it's gonna be a race to get people into town to buy every super capacitor from every store they can get to, and then get them charging from the windmills.
The Mormons will easily show up before they finish, but with any luck the mutual "hey, hello! Welcome!" picnic and potluck, sharing of hot dishes, and general friendly meet and greet will go on long enough to charge the device and render modern technology obsolete for thousands of miles around them.
The Mormons have a culture of anthropological scholarship, a byproduct of their missionary programme and (to a lesser extent) of disproportionately many Mormons working as intelligence analysts. As such, it’s not implausible that they might see through such a ruse.
It may do the Amish well to start quietly hoarding supercapacitors as soon as Amish-Mormon relations start souring. Or even before: one could make a case for a preprepared EMP bomb being the Amish equivalent of a nuclear deterrent against any potential aggressors.
I'd definitely agree that the Amish would be well served seeking enhanced second or even first strike EMP capabilities.
I don't think the picnic would be taken as a ruse however, only as an unavoidable preamble to any group interaction. My, admittedly limited, interactions with Mormons led me to believe they also have a cultural weakness for the potluck.
So less a ruse, and more of an ambrosia and corn themed version of 1700s troops lining up before battle.