I don't know why you feel it appropriate to adopt such a tone with me. I'm starting to suspect that you are less interested in learning the correct answers, and more interested in advancing some sort of kook science agenda.
Gauss's law applies to electrostatics, not moving charge.
Gauss's law is absolutely universal. In fact, it's one of Maxwell's equations.
Apply Gauss's law to a current carrying wire. The integral of E over the cylindrical volume is zero, is it not? That means there's no net charge enclosed, as is true in an electrically neutral conductor. Yet the measured E field is in the direction of the current travel is it not?
Yes, but the integral of the field, as you point out, is zero, thus Gauss's law is satisfied. I'm not sure why you bring this up in any case, as there is no gravitational analogue (any mass current will have a net gravitational charge, as there are no antigravity charges).
E is in the direction of the current density. The wire has a net E field,
No, it doesn't. You correctly stated above that the integral is zero.
but net zero charge. Where would this net E field come from if the total electrostatic charge of the wire is zero? Why does it exist only when the charge is moving?
That's just wrong. Moving current in a wire does not create the electric field; rather, the electric field causes the current to flow.