Meg, I haven't found any connections with NY/NJ Kachelriesses, but that doesn't mean there aren't any!
I've also found Kachelreiss and Kachelriss -- but they are all the same original German surname: Kachelriess.
This name is so very rare in the old country - I'm told that virtually all of this surname originate from the same area in or near Unternesselbach, Mittelfranken.
None of the NC Kachelriess descendants used this spelling. In every case they used the anglicized spelling. Some of the variations are: Cocklereece (my line), Cocklereese, Cocklerees, Cockelrees, Cocklerease, and Cocklereas. I descend from Michael Kachelriess, his son, Daniel, his son David, his son, Henry, his son Martin Luther, his son James Levi (my father). The only records that use the Kachelriess spelling are the Friedens Church Records (Guilford County, NC) which were originally written in German in the early 1800's. Later records records written in English spelled it Cachelris and several other variations.
Orange Co Tax records spelled it Cocklerees.
Census records spelled it Cockleruse, Cocklereece, and Cocklereese (among others...)
Michael appears as Cockleriece and Cocklereas in NC probate records.
Daniel appears as Reece on the 1850 census.
David appears first as Cocklereese, then as Reese. His son Henry appears as Reese and then Reece -- his children used Reece, Reese and Rees... His on Martin Luther, appears as Reese and Reece, but all of his children used Reece...
My father knew his great grandfather had changed the name from Cocklereece to Reece, but didn't know the name was actually Kachelriess. I'm certain the majority of the Cocklereece ancestors had no idea how the name was really spelled!