All the wiring is fine. I even removed the tailpiece bushing and the ground seemed to be making good contact.
I considered eliminating the grounding loops, but with such a daunting task, I followed some instructions on shielding and glued some aluminum foil in the electronic components cavity. And what do you know, the noise is gone!! All of it! There still is some noise when I crank the amp, but that's normal. Thanks for reminding me of that page, I didn't go there first cause I remembered it was just strat stuff. But it turned out to be a big help.