I finally made it to Elmora Churrasqueira in Elizabeth (near Union). It is just off Elmora (thus, the name).
They have a big grill with real wood charcoal (saw the bags) and flat wire racks that they put flattened chickens into which then spin around like a rotisserie. They also make chourico, pork ribs, steaks, quails.
The place only has a few small tables and on Saturdays and Sundays, there can be an hour wait between placing an order and the time it is ready (they warned me) as many folks order ahead and then come by to pick up their food. Maybe they will be a little calmer when a new "pollo a la brasa" place opens up on Elmora.
I wouldn't drive hundreds of miles to go there, but it was tasty enough if one is in the area (and patient).