First of all turn your plans around. Most dive operators do the SRC dive in the afternoon after doing 2 tanks in the morning. Takes about 20 mins. to the dock on the Sound from the port (most have a shuttle) under 1/2 hr. for the ride out plus it's a fixed 45min. dive. So you're easily back by 3PM or sooner. Any of the operators working the cruise trade know the timing to get you back better than you do - they deal with it every single day.
Little Cayman is out of the question on your time frame. It's only a short flight but the logistics of that would be impossible with the flight schedules - you couldn't arrive soon enough for the morning boats and you couldn't get back in time from an afternoon boat to fly back to GC for your sailing - much less adding in SRC. They want you checked in an hour b4 the flight and the cut-off is 30mins. before. I'm not positive but I think they pressurize the plane also so no-fly rules would apply. It's not even realistic to try.
Eden Rock/Devil's Grotto is an unspectacular dive that happens to be 500' from the cruise port. Unless the silversides are in in Summer. Then the
Grotto is pretty great. IMO it's the worst dive we did on Cayman all week. Decades of cruisers haven't done it a lot of good.
Many of the dive operators do 2 tanks in the morning then SRC in the early afternoon.Reliably most will take you to the best site they can reach weather permitting. Typically they'll do a deep wall dive then a shallower 2nd - often that depends on the make-up of the divers on the boat. Since there can be 4-5 cruise ships in port daily, that's hard to predict.
Foster's is the Carnival Cruise operator. Their contract requires you book thru the ship. Located slightly south of Georgetown they have a shuttle for their cruise pax.
Don Foster's Dive Grand Cayman
There's also 3 dive operations working near the Lobster Pot dock/operation -
Lobster Pot Dive Center - Grand Cayman Until this most recent website re-design they had a cruise diver section - IDK why they don't now. It's a few minutes walk north of the port.
I've recommended
Wall to Wall based on knowing the owner slightly.
Deep Blue also gets good recommendations. You can walk over and with a 7AM port time there shouldn't be any problem getting on their morning boats. The other option in that area is
Off the Wall Divers. Any of them are 8 divers max/boat - not so with Fosters. Everyone on Cayman provides a DM per 8 divers - it's the CITA rule.
Cruisedivers is another option - they offer the 2 tank plus SRC returning at 3pm. Also walking distance north of the port.
Pre-book whatever you decide to do.