It may be too late/expensive, but we have flown into Beef Island to avoid the ferry schedule madness. They might make the 2:15 Smith ferry, but I wouldn't count on it. I like the idea of an afternoon ferry to Jost, just have never looked at it. We have checked in to C&I there at Great Harbor, but always from our boat, never a ferry. You could move the boat mid-day to make sure you get a mooring, then hit a good lunch place.
If they can get to and through West End at a reasonable hour, I'd say go to JVD. If it's full, head over to CGB for the night. It can be noisy late, but restaurants are welcome after flying, getting organized, etc.
I would avoid Cooper that late in the afternoon. Hard to get a mooring and, if you do, playing bumper cars all night after the wind dies is no fun.
Our MarineMax 443 in April was fairly fuel-efficient at 10k, but not at 12-14, so we kept close to 10. Still, West End to JVD would be 1/2 hour, a bit over an hour to Norman. In June, there should always be a mooring in the Bight.
Most of all, remember it's island time. It doesn't work to fret, so just enjoy.