Josh - your angle might be better if the wind
is anything north of east. But remember that the reef around Anegada has grabbed over 300 known boats so you'd either need to sail around the north of the island (better angle but longer distance) or sail quite a bit south to the clear the reef and that would put you just a few degrees better than the sail between Virgin Gorda and Neckar Island.
I would agree with Mark and Teknav, I've cleared in at the Capitainerie many times and I can't really recall
time where they looked at my papers.