The discussions in this thread make me wonder... it seems like the
tough part of making variable caps in the "classical" shape is making
the plates. In my distant past, I was involved in making modest
quantities of punched aluminum parts, and found a shop that was willing
to make a punch/die set for the parts, even though my initial order was
for only a couple hundred of them. (Eventually I ordered enough to
wear out the punch/die set and they made another one...probably did
10,000 or so total.) Once you pay for the punch/die, the parts become
pretty cheap, and the uniformity is vastly superior to what you could
reasonably do by hand. So, the question becomes, if the plates (rotors
and stators) were available in maybe two or three different basic
sizes, how many frustrated hams would be interested in buying them?
Might it be enough to make the punch economical? Would you be willing
to pay, say, two dollars per plate for 0.0625" thick plates with 3"
rotor diameter? A set of 25 such plates, using 0.1" gap (good for
maybe 7kV peak?--provided the edges are properly rounded), would give
you about 190pF. Do the people who would be trying to build such
things already have the ability to do the rest of the parts, or would
they need to be included too? Does someone already sell kits of
capacitor parts?

That's obviously way beyond what the OP needs for a receiving loop, of
course! For that, I'd probably use a varactor diode...or find a radio
receiver to scrap one out of if I wanted to stay mechanical.

Cheers,
Tom