Sorry about the delay. I had to find a wiring diagram first so I could see what you have there. Those 3-wire regulators add a bit of complication to the alternator conversion, but the problem should still be fixable.
This is only a test to see if the alternator will charge at all. Disconnect either battery cable, so you don't accidentally get a short while you are working on the wiring. At the old regulator connector, connect the blue and yellow wires together. Don't connect anything to the red wire. At the alternator, connect the blue wire to terminal #1 on the plug-in connector. Run a short jumper from terminal #2 to the BAT terminal on the alternator.
Reconnect the battery cable and start the engine. Check the charging voltage with your voltmeter like you did before. If the voltage reads normal, shut the engine off and remove the jumper from terminal #2. Now run a new wire from #2 to either the junction block on the horn relay or the red wire on the old regulator connector, whichever is easier. This wire carries almost no current at all, so it doesn't have to be very heavy. 18 gauge will be fine.
There is a possibility with this hookup that you may not be able to shut the engine off with the key. If that happens, pull the plug-in connector at the alternator and post here again. Don't be too concerned about this, because the fix for it is fairly easy.
Ray