No fertilizer going into winter in general. I bet cold hardy green giants might stand it but why risk having fresh tender growth when winter comes. Far as your branch goes,w/o a pic I say properly prune it back just outside the branch collar. reattaching it would take a grafting like approach and need to be done almost immediately this time of year. Low chance of success and lots of trouble. Sorry for not being more chatty, on the cell.

Coming in a bit late to the party but I'd agree that these trees are most likely exhibiting various degrees of drought stress. By default, just because of their structure and elevation, raised beds or berms drain more rapidly and retain less moisture than does a level, inground planting surface. More frequent watering under even normal weather conditions is usually required for these sitings. And NJ did experience a hot, dry summer. Even now (1/7/16), there are areas of NJ that are still under a drought 'watch' designation. I agree with Mike that some periodic deep watering (low and slow) during the summer months would have been very appropriate. And very likely would have prevented this discoloration and drying you are seeing now. And Ken, you are correct in your assumptions about root growth in winter. Root growth is very seasonal, generally presenting in two surges - prior to shoot growth in spring and and later in the summer after the cessation of shoot growth. Soil temps do have a bearing on root development and both root elongation and the development of new roots comes to a halt when soil temps drop below around 40F. So the ground doesn't even need to come close to freezing before root growth stops for the season.

I am late to respond, but I just stumbled on some Green Giants at the nursery at Canadian Tire, of all places, in Midland, ON ... this suggests to me that they are more widely available now. (I have been trying to find them for a number of years and this is the first time I have actually seen them.)

if its not browning.. its not dying ... its probably.. for whatever reason.. focusing all its energy growing roots ... why this one of the bunch.. who knows .... its not surprising there are all growing the same.. the kids dont.. so why would the trees ... i dont recommend digging it up to find out why ... it simply isnt bad enough to risk such ... most likely.. it will catch up .. its a conifer.. and its a tree.. and they grow in tree time.. counted in decades ...6 or 7 mont6hs is nothing .. and.. again.. its green and doesnt look like its suffering.. stressed ... so just leave it alone ... imo.. fert is not a response ... just check for proper water at root level ... i would pull back the grass for at least a 2 or 3 foot circle around it.. and then you can take a hand trowel and check moisture at 3 to 6 inches ... hard to believe the grass overgrew the planting hole in said time .... if for no other reason ... get the grass out ..... so you dont have weedwhacker issues on the trunk ... just be patient .... ken