Palm Beach/Lake Worth Inlet is the closest distance to West End, which bears due E, about 60 NM. However if you leave from other inlets further south, you'll get a lift from the Gulf Stream instead of having to head S of due E to compensate for a 2-3 kt current.
Early morning crossings are best (like leave the inlet at dawn.)
If wind is out of any northern quadrant, stay the hell out of the Gulf Stream! A 5-10 kt wind from NW, N, NE is much worse than a 15 kt SE, S or SW wind.
Mid-July is statistically the least wind and also lower chances of rain than June. August is getting too close to hurricane season.
Lake Park Marina is a decent place to leave boat.
Considering the expense & amount of prep work required just for a crossing to West End, you might as well press on another 40 NM to the Abaco's, which have much better diving and fishing! Although Walkers is essentially abandoned (although I think Snookerd said they had customs guys there?), gas and other limited supplies are usually available at Grand Cay.
Beware of having a schedule, the most dangerous thing you can have on a boat! Most folks get into trouble or have rough crossings because they don't have the flexibility to wait for good crossing weather!
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