Brian, when I lived in northern New Jersey when there were many woodcock along some of the marshy rivers and streams, I used a 28 ga. Beretta BL-4, 26" barrels imp.cyl/mod with mostly #9 shot. Sometimes I would use a Win. 101 20 gauge 26" barrels imp.cyl/mod. same shot.
Early season birds usually held good and most shots were quick as they loved to zig-zag through the trees. Later on in the season maybe 30 yards and again the same zig-zag.
A good friend of mine went down to Cape May during the migration, the Woodcock gathered there waiting for a south with to carry them over the Chesapeake Bay. He stated getting out of the car and closing the door woodcock would flush all around, the cover was very thick and you earned your limit.
I think that your experiences and preferences are right on. Good Luck, I missed hunting them when I moved to eastern PA.