We have done the trip a total of four times in late Winter/early Spring and going due East through the NE Providence Channel, as Jon suggests, was far easier than the 'Thorny Path'.
On one trip we sailed NE for 2 days, towards Bermuda, after we passed south of the Abacos. It is an error to sail SE too early as it ultimately gets you into the current sweeping north of Hispaniola. On two occasions we were able to turn SE at 67W and lay St Thomas.
Going on the backside of a front not only gives you better winds it gives you longer before the next front can complicate your life just as going north can get you closer to the center of a winter low.
While many cruisers use Chris Parker for weather routing we just use Sailing Weather - Marine Weather Forecasts for Sailors and Adventurers - PassageWeather
for all our East Coast and Caribbean routing/timing.
Good luck Phil