[1] The Feds are lying?

Of course, what self respecting buearucrat wouldn't lie to cover their ass. About what remains to be seen.....

[2] The USCG in the NJ waters had a faulty radiation-detector?

Probably not....

[3] After the initial radiation detection, any radioactive contraband onboard was tossed into deep water overboard [at night?] by the crew?

Again, I think not. I'm sure they had this boat well watched, night or no night.

[4] Cosmic rays?

There is always a cosmic ray background. A spike in this signal large enough to approximare a local source would have other ramifications that would make a dirty bomb the least of our worries.

[5] Or the ship really did have radioactive contraband onboard for sufficient time to induce temporary radioactivity in the slate-tiles cargo, prior to the ship reaching American waters...And before the USCG could approach to within visual or radar-range
of the ship [within 200 miles of the NJ coast] a Zodiac was used to take the radioactive contraband off the ship.

A geo buff tells me that slate is a metamorphic rock formed from sedimentary layers. Not exactly where I would expect a sizable natural radiation but maybe the detectors are REALLY sensitive.