Since your alternator charges with the regulator bypassed and you've tried several units, the problem would appear to be with the wiring - not the regulator/rectifier or alternator coils. How have you connected it? I believe this is a drop-in replacement to plug into the stock rectifier cable, with the two loose wires meant to connect to the stock harness wires for the original regulator. The green regulator wire is not used with it.
The wires on the plug are 3x yellow for the 3 stator coil wires plus green to frame and red to battery +.
The loose black is for switched power and white is for the field coil. The most likely problem from your description is that you don't have switched +12 on the black wire.
Depending on which type of regulator it is, the other field coil wire goes either to ground or switched power. You have it grounded (you say it charges when white is held to +12).
Stock SOHC 750 regulators ground the field coil, DOHC and many aftermarket ones connect it to power.
If you confirm the black wire has switched +12, possibly your regulators have all been the "other" kind.
Since this looks like one designed for SOHC engines it should work with your bike normally, but check with a tail light bulb if it will light from white to battery +. This should not damage either type of regulator: the "right" kind will light the bulb from white to ground (with key on) and the DOHC type should light it from white to +12.
If it is the rectifier polarity, just connect the field coil return wire (also white at the coil but it goes to ground somewhere in the harness) to a switched +12 wire (standard color is black). Field coil connections are non polarized, + and - can be either way.