There does not seem to be any decent road to do this. If you had a trail bike or perhaps a 4X4, you could turn off N at Cruce de Ocoa and then after getting to San Jos? Ocoa, take a dirt road through to Jarabacoa, but is would surely take longer. This is very mountainous country. I think there is a motorcycle video of this road that Frank12 made a while back. The road from Cruce de Ocoa to San Jose de Ocoa was recently redone, but beyond there it is more like a track or a trail. It is certainly more scenic. I don't think there is any guagua or bus available out of San Jos?.
There is a trail laid out by the Americans back in the 1920's when they dominated both the DR and Haiti that more or less follows the Haiti/SD border. Cobraboy posted a video of his trip along some of it. It is a trail that would be easier on something with hooves than tires.
Santo Domingo is sort of the hub of everything. All roads lead to Santo Domingo.
I do not claim to be an expert, perhaps someone else has a better answer.