I am aware of the byzantine procedural rules.
I did draw a map. I don't have a census block map for the county (just a voting district map), so the lines are approximate as to where the chops lie in the town of Kinderhook and Taghkanic.
If I assume a 5% max deviation to get to a 10% range, Ghent is too small to be a district on its own (-6.8%) but Claverack is just barely the right size for a district (+4.97%). I presume that you've compensated for Ghent elsewhere, but why not make Claverack whole instead?
With Claverack whole, the Greenport district would pull about 1000 from Hudson and 600 from Livingston. Ancram, Gallatin and Taghkanic would pull about 1200 from Livingston. That leaves the rest of Livingston with Germantown and Clermont. It's the same chop count in the south but removes the ugly connection (IMO) between Clermont and Gallatin.
In the north you would have to add a chop to bring Ghent up at least 46 people to get the range within 10%. OTOH you could probably make a case of a compelling state interest to accept that extra deviation for a range of 10.79% to keep Ghent whole as a district.