So you vreg is supplying voltage to the alternator field. And, you know that voltage is reaching the field coil, yes? Now you have to see why the power the alternator is making, is not getting out to the system.
This means measureing the three yellows.
Either do an ohms test for the stator wires (dead system) at the vreg connections.
Or, measure the AC output coming from the alt to the vreg,
Next, you will measure each of the six diodes to verify they will only pass power in the direction of the battery. 12 tests using the diode test function on your meter, between each yellow to green and each yellow to red, repeat with probes reversed.
Have you verified that the engine has a solid electrical connection to the battery NEG terminal?
Cheers,