I've seen and heard American Woodcocks in 2 Washington County locations 3/30 and 3/31:
Lake Elmo County Park - main road in to T, turn right and go towards the fishing pier. From the road I heard at least one calling to the right.
South of Big Marine Lake, between 1.0 and 1.1 north of County 7 (Square Lake Rd) on May Av. N.
Big Marine County Park is a relatively new Washington County Park. I checked it out 3/31. It's small but has some nice habitat and offers good viewing locations to scan Big Marine Lake. I saw a few migrants: Tree Swallows, A decent mix of ducks, Common Loon, American White Pelicans, Fox Sparrows. The park's entrance is on Manning Av. just north of County 4.
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