I had a go at it, hope you don't mind. And I think we should definitely go for NE first:
Note that this requires that we chop and build the cottage before we road the sheep, which means we must cancel the Crab gift to Washington in two turns. But I think that's a fairly low price to pay.
Spoiler :

Note that this requires that we chop and build the cottage before we road the sheep, which means we must cancel the Crab gift to Washington in two turns. But I think that's a fairly low price to pay.