I assume that this is without any extra electrical stuff turned on, correct?
It seems hard to imagine that a slipping fan belt would cause this, although I suppose it's easy to check. In my experience, when a fan belt slips you know it, because of the screech, and it seems unlikely that it would suddenly slip so much that the output, at 3500 rpm, would drop essentially to zero. When the red light is on, that indicates that virtually all output has stopped.
Since the output is OK at lower speeds, it's unlikely to be the generator.
That just leaves the control box. It's possible that the regulator relay is sticking, or some other flaw. The resistor (which is located on the underside of the box) could be burned out or otherwise disconnected. The fact that it's new doesn't matter much, in my view; I never assume that new components are good components until it's proven to me.