We usually book with DYC/Navtours since we like their catamaran options better than the Moorings. The Exumas are more expensive right now than other destinations. Moorings probably a bit pricier but not by much.

I'd plan for 5-6 hours to cross the Yellow Bank, but it really depends on wind speed/direction and if you plan to sail or motor. If the wind is light out of the east, might take you a bit longer if you sail. As far as seasickness, just depends on the weather. You'll get more protection the closer you get to the cays under prevailing conditions. We motored across a few years ago with the tail end of TS Alberto giving us 20+ knots on the nose. Was not fun for some of the crew, but everyone preferred that to staying at Palm Cay an extra day.