I’m going to wind some new coils and see how they compare to the old ones. These will be superior in a couple of ways: better cores, and better winding technique.
The cores will be these ferrite rods (replacing the hot-galvanized nails I used the first time. These are the rods: https://www.walmart.com/ip/5Pcs-Mn-Zn-Ferrite-Rod-Bar-Loopstick-For-Radio-Antenna-Aerial-Crystal-AM-5-5-x0-4/855082587
For the winding technique, I’m working on building a winding jig out of plywood. The idea is to make a gear system out of wooden gears using the approach detailed here: https://woodgears.ca/gear/howto.html
A crank handle will turn the gears, which then turn a cheap drill chuck that will hold the workpiece (in this case one of the ferrite rods mentioned above). Wire feeds onto the rotating workpiece from a spool after a tensioning device applies tension to the wire. I’m not sure what I’ll use for a tensioning device yet, but it could be as simple as a series of holes or pegs for the wire to pass through or a clamp that squeezes the spool of wire. Having a set of gears allows me to get several turns of the workpiece for each turn of the crank.
I used a different template generator the create the gears than the one provided on woodgears.ca. It creates involute gears, which aren’t as easy to cut out, but transfer power more efficiently: http://geargenerator.com/
I drilled and cut out the gears using a drill press and scroll saw. They’re not perfect, but they may answer the purpose. If these don’t work well, I may try again with the woodgears.ca template generator, which creates less complicated geometries for the teeth.