I’ll give it more thought, but I did Great Barrington to the trail (camped at Taconic Copake) last September on an Sunday afternoon via Rte. 23 from MA into NY. Thinking it would not meet your criteria. Shoulder gets narrow in places, and there was a good amount of traffic. The trail is terrific. Especially the recently completed section north of Millerton. Taconic Copake is also a very nice place to camp. The new bathhouse is amazing.
Here is an option to bypass the a lot of NY 23 in NY that I was looking at a couple weeks ago in connection with a thread on another forrum:
GREAT BARRINGTON-HVRT - A bike ride in Egremont, MA (ridewithgps.com)
The portion of MA 23/NY 41 to get to the turnroff has a good shoulder, IIRC. You can view it on Street View and judge for yourself. As you can see, there is about 2 miles of unpaved surface. Some of that on the descent is
really steep. From mile 4.82 on the surface can be seen using Street View. Obviously no shoulder, but I cannot believe there is heavy, fast traffic. In hindsight, had I realized this option existed last year I would have tried it. Roads like that can be a real gem.
Ooops. Now that I look at Satellite View i appears that Orphan Farm is gated at the intersection with Mountain. The west end is open because that's where I got on the trail from NY 22. No biggie. You could just stay on Mountain and pick up the trail where it crosses that road just by the park entrance. The portion of the trail from Orphan Farm to the park entrance is not a must-ride. South of that point is. A friend of mine and his wife just happened to ride it two days before I did. They had to stop for a bit until a bear in the middle of the trail decided to move on. The store/cafe along he trail across from the park entrance is nice.