I'd look really hard at Belize. It's about 8+ hrs. from SEA with one connection both ways.
Excellent diving, sharks, all sorts of nice reef. The bucket list adventurous can dive the Blue Hole but Turneffe and Lighthouse are the best.
If you want to do an AI there's a lot of them on the atolls. Most pick you up on the mainland and you dive/stay there all week. They get you out to the best sites nearby. Turneffe Island Resort, Turneffe Flats, Blackbird Cay, Thatch Cay - all are options. And there's more.
You can also stay on Ambergris at any number of resorts from simple to upscale or move south to the Placencia area.
In late spring/summer there's whale shark diving off Gladden Spit - the only place you can
dive with them in this hemisphere. For that you need to stay in the south - it's too far from Ambergris. There are longer boat rides from that area out to the reef but nice beaches. Places like Hamanasi, Roberts Grove, Turtle Inn are very upscale, more affordable is somewhere like Laru Beya. In that area Splash Diving is a good option - they also bundle packages with some local resorts.
One advantage that area has is there's a lot of non-dive activities that are accessible. Ziplining, cave tubing, Mayan ruins tours, the Jaguar preserve, Howler monkeys, river tours, Cockscomb Nature Preserve. Even the Belize Zoo is supposed to be worth a look.
You fly into Belize City and there's a second short flight to either Ambergris or Placencia. On Maya Island Air those are usually overwing
turboprops or smaller
Cessna Caravan planes to the smaller airports. There's also a ferry to Ambergris.
One thing I forgot to mention about Grand Cayman is that with any sized group above 6-8 you'll basically be a private charter with most of the operators - except Red Sail or Fosters who handle the cruise traffic. So your group will be able to specify dive sites etc. Actually a private charter might actually be cheaper when split equally.
---------- Post added November 2nd, 2014 at 10:46 AM ----------
Dont know about from the US, but theres definetly not just "very small planes" flying to St. Maarten though...
Did you watch the video? My point was that
from St. Maarten - which I know is served by large commercial jetliners from the States -
to Saba requires a flight on WinAir. On one of these:
http://www.wings-aviation.ch/03-Reports/2011/NED-St-Maarten/DHC-6-300-01.jpg - an STOL aircraft. Any sort of group and they'll need to add a plane or two. And there's luggage restrictions also to deal with.