Interesting. Perhaps test the it with a home made jumper wire grounding the mounting screw of the voltage regulator directly to the body somewhere. Not to the dash though, as it could have a weak ground too. Do it directly to the firewall perhaps.
And speaking of the firewall, is your battery grounded to the body as well as the engine block? A necessity is to have a wire going straight to the body from the battery. And a really good practice is to upgrade your stock grounds with a strap or wire from the back of the intake manifold to the firewall.
This is a long shot for your gauges, since the regulator doesn't use much current, so really should not need much of a ground to function properly.
But it can't hurt to try it!
And last, but not least... I'll go back to one of our Bronco-mantras, and that is that "new' no longer means "good" when it comes to parts. So your brand new voltage regulator could be faulty.
Since most fail by putting out too little voltage rather than too much, it would be quite the coincidence for your old one to fail to 12v output, and your new one to do the same thing.
But it's not impossible either, so should not be ignored.
As a bench test you can connect a battery to both of your regulators. Negative to the case, positive to the input connector. With it grounded directly to the battery like that, you should see exactly what the regulator is doing independent of any gauges.
Hmm, and speaking of gauges... Maybe Viper or someone knows this, but if one of the sender wires is shorted directly to ground without going through the sending unit on it's circuit, what would that do to the regulator output?
Seems like it would still only put out as much as it's capable of, so if it's putting out only 5v it should stay that way. But if shorting to ground causes it to just pass the full voltage through it, you would see the same on the output as you do on the input.
Maybe one of the experts will chime in on that possibility.
Paul