Crossing from Bimini would definitely be faster than trying to cross directly from West End to Port Everglades. In order to compensate for the GS the later route
would likely be more than 80nm (depending on your speed) while the crossing from Bimini would be less than 50nm with a strong boost from the current
The alternative would be to cross from WE to Lake Worth
and then go down to Ft. Lauderdale inside. I did that trip on a friend's boat a number of years ago and it was a real PITA with all the restricted bridge openings. It took us all day to get from West Palm to Ft. Lauderdale. That was on a weekend with no rush hour restrictions, but with a gazillion other boats waiting at each bridge.
I guess you could hug the beach and go outside from Lake Worth
to Port Everglades, but I think you will pick up some of the GS right off the Lake Worth inlet.
Best not to fight the GS or the FL bridges and start from Bimini.