After some good opinions, and advice, I'm currently winding a new test coil.  In this coil the core will be made from straight pieces of annealed welding rod.  After annealing the rods I coated them with lacquer.  Once the lacquer was dry I spread them out, covered them with thick slow super glue, and quickly bound them together.  I should have used epoxy here.  I also have a feeling that the coat hanger wire will work better, especially after annealing it.  Next change, will be upgrading to 18.5 AWG wire.  This coil will probably be longer, so I can get about 300-400 windings of the thicker wire on it, and I'll have taps at every 100 windings.  I'm thinking that in the finished alternator all the coils should have taps.  This will add some flexibility for applications at different RPM.  For certain applications, like small water wheels that run real slow, and put out very little power, an output of 1 or 2 amps at ultra-low RPM could be excellent.  Since water wheels run 24 hours per day, very low output of a couple amps or less can really make a difference in a home power system!  When finished, I'll test this unit on the primitive machine pictured.

This machine is nothing more than a log across the creek with a notch cut in it.  The water runs through a squirrel cage from a furnace.  It puts 2-3 amps into 12 volt batteries 24 hours a day(about 40 amp/hours).  (through long-thin wire, there is about 50 yards of 12 gauge between the water wheel and the batteries) Another big inefficiency here is clearly the V-belt.  A good low rpm alternator might solve that.

I welded a "coil holder" that would fit the tool holder of the lathe, such that I could carefully place the coil between the two armatures.  Each armature is about 3.625" diameter and has a ring of 7 magnets.

I next performed a few tests.  I tested the difference between using single stacks of magnets, or doubling them up.  Doubling them up improved almost all the readings by about 20%.  I added a bridge rectifier, and connected the output to a capacitor.  My thinking is that in the final alternator, this capacitor will allow the coils to be hooked in series, and be out of phase slightly.  It should also reduce electrical noise.  With this setup, 600 rpm, with the magnets stacked two high, the coil put out about 2.5 amps into a full charged car battery.  As before-, the tradeoff with less windings was higher current for less voltage.  At 400 windings, it would put 4 amps into a short circuit.  I might add, the bridge rectifier was only rated 4 amps, and it was getting hot.  I never tested this outfit on AC, except at the very beginning.  At 600 RPM, open voltage at 300 windings is about 22 volts.