The map below shows why it was so windy in April on the North Slope (graphic courtesy of Brian Brettschneider). The sea-level pressure was the highest on record for April over the Beaufort Sea, and yet the SLP was below normal over nearly all of Alaska, and well below normal over the west and southwest. Consequently the pressure gradient across the North Slope was intense.
The record high pressure north of Alaska in April is intriguing, because it occurred in the wake of a remarkably strong stratospheric warming event back in March. It is well-known that sudden stratospheric warming events create high pressure anomalies that propagate down to the troposphere over the course of several weeks, and so I suggest that there was a chain of causality between the upper-level warming event and the April high pressure.
The following figure illustrates the downward propagation of the flow disturbance in the recent event; this is a time-height cross-section of geopotential height anomaly over the Arctic (a height anomaly is equivalent to a pressure anomaly). Beginning in early March, a pronounced positive height anomaly emerged high in the stratosphere, reflecting the complete breakdown of the polar vortex that occurred in the dramatic "sudden warming" event. Note that earlier in the winter the stratospheric vortex was extremely strong (i.e. lower than normal heights), as we noted in December.
It's pretty clear from the figure that the height anomaly propagated down from the stratosphere to the troposphere and eventually to the surface between mid-March and late April. Again, this is a typical course of events after a sudden stratospheric warming. As an aside, this provides an unusually extended and useful window of predictability for high-latitude weather patterns in the troposphere.
The map below shows the standardized height anomaly at 850mb during the first 3 weeks of April, when the wind was particularly strong in Barrow. The high pressure was centered about 500 miles north of Prudhoe Bay and produced a strong easterly flow along the Arctic coast of Alaska.