Question[s] #5
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We are having a hard time approximating the wind at our ship's position when using a formula we found requiring change in 
geopotential height over a distance (plus gravity and f). We are getting winds at around 40 m/s at the initial position at 
500 hPa, which we know is wrong. Is there another level or method we should be looking at to approximate the surface wind?

Answer to #5
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The geostrophic wind at the surface will depend on the pressure (geopotential height) gradient, which depends on
how much (or little) you think the central pressure (height) at the cyclone center has changed over the 6-h 
period. To simplify the problem, you might make an assumption about pressure (heights) at some distance from the
cyclone center that makes calculation of the pressure (geopotential height) gradient possible. Geostrophic wind
direction only depends on the shape of the isobars (geopotential height contours) about the cyclone center. Be
sure to clearly state any simplifying assumptions that have been made in making your calculations possible.
And I don't quite understand why you mention the 500 hPa level position, the ship is impacted by low-level (1000 hPa) winds.