I would think even a lower end category 2 would produce damage near the catastrophic end. A category 3 could probably make some areas unlivable for months, especially the shoreline. You would think power outages would persist several weeks in the hardest hit areas and you would probably be looking at >80-90% power outages for several days to week.
I agree with pretty much everything you said here. These would be the conditions needed to facilitate such an event. Of course too exact track and where landfall were to occur would dictate just how catastrophic an event would be.
One other factor to consider too is climate change and warmer waters, especially south of Long Island. If we were to ever see a strong hurricane moving up the coast, it may not weaken like it would have before, especially if the forward speed is quite fast.
It really is just a matter of when for such a scenario to occur. I guess we can only hope that if such a storm did come up the coast it wouldn't make landfall and just brush off with the center passing east of Cape Cod. We would still get pounded but that might prevent a total worst case scenario...?