Doesn't seem very likely!
Our NJ roads, pretty much suck - even though we pay exorbitant taxes. Wonder where the money goes.
Also, riding bikes on sidewalks is not a good idea and it's illegal in many places. For example, downtown Princeton has signs posted. Of course you wouldn't want to ride there anyway, since there are lots of pedestrians.
Here are a couple of suggestions for mostly low traffic roads.
I assume you got to the Griggstown Causeway (where the canoe place is located) via the tow path along the D&R Canal. If you get off the tow path at that point, you have no choice but to ride narrow high speed shoulderless roads (without sidewalks). Both Canal Road on the east side of the canal/river and Millstone River Road on the west side are like this.
If you take the tow path south you eventually get to Trenton. There's some riding on roads in Trenton (take a map or GPS, because the path is not well marked), and the path eventually connects to the feeder canal tow path which you can take all the way to Frenchtown. At Frenchtown, you can walk your bike across the bridge over the Delaware River to Uhlerstown, PA. There you can connect to the tow path along the Delaware Canal. At this point, I have only ridden south. However, I understand this tow path goes north at least to Easton. At that point you should be able to cross back to NJ and look for a way to get to the Gap.
For your specific question, Griggstown Causeway to Hopewell Wertsville Road, the first thing to note is that Hopewell Wertsville road does not meet your criteria. It's the main road north from Hopewell over the Sourlands into the Amwell Valley. It's 2 lanes, no shoulders nor sidewalks, and fairly high speed (45mph, I think). On the plus side, the portion of the road which climbs out of Hopewell has just been repaved. I occasionally ride a loop that includes Hopewell Wertsville to Griggstown Causeway. Here's a link to one of my rides on ridewithgps
. Dutchtown Zion Road is a dirt road for roughly a mile after the junction with Long Hill Road. In the direction I go, it's downhill. You would be going up hill. On my to do list is to check out Long Hill to Hollow to Grandview to Pin Oak to Dutchtown Zion to see if that's a good way avoid the dirt part. An aside: Hollow Road is a pretty route from Route 518 into the Sourlands. A good part of it is along a brook and since you're going uphill (slowly, at least in my case) there's plenty of time to enjoy the scenery. End of aside. The linked route does not meet your criteria, but I doubt you'll find anything that comes appreciably closer.