Interesting, I'm right in the middle of this, so very timely, thanks for posting.
As a surprise to me, the price of variable capacitors (which you can pair with an inductor as described to get a particular resonance) has gone completely through the roof because apparently nobody uses them any more. So what used to be a 20 ct part is now $7,50 quantity one and quantity 50 as well!
You can see a couple in the picture of the regency radio, the circles with a screw in the middle. The ones in the other radio in the little metal cubes are adjustable coils, they have a split ferrite element that screws up and down to extend the length or contract it.
As for stripping the conductor of the enamel: the best and safest way is not to scrape or sand (which will affect the conductor by reducing its strength as well as its cross section) but to simply boil off some of the enamel in a bit of solder stuck to the tip of your soldering iron.
That way you only strip just as much as you need to and there is no mechanical damage. You also should not twist the two wires the way it is done in TFA because these coils will pick up LF noise as well and that will end up rubbing the wiring to the point that you can get a short. The easier way is to just put a drop of superglue on the paper that you're going to use as coil body and then to stick the winding end in it and wait for it to dry (which should be really quick). After that you can start winding.
Wind nice and tight and make sure to not leave any air between the coil body and the ferrite, this will result in 'microphony', your core will end up modulated by sound waves! That's why if you're going to wind around paper you should wind with the paper already around the ferrite as tight as you can make it. If the paper slides on the coil too easily then you may have to mechanically affix it to make sure that the microphony effect is minimized.
If you need to cut ferrite realize that the stuff is super hard. It is easier to score it using a grinder wheel (a big one, or one on a dremel) all the way around and then to snap it off. After that you will still need to dress the ending, the fragments are super sharp so be careful you don't cut yourself.
Finally, I hotmelt a little piece of perfboard onto the ferrite and then solder the coil wires onto that and exit using thin silicone wiring. That gives a very flexible interface which will result in fewer broken coils.
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