...what could these divers have reasonably done differently...
For the sake of discussion, sharing ideas and learning, I would point out that most believe the key is PREVENTION. This includes; listening to the pre-dive briefing, following the instructions of the divemaster(s), sticking with the group, and returning to the boat at a designated time. Please know I am NOT saying that the divers in Antigua didn't do all of those things and it would be foolish to speculate. Right now, I am just doing the "what if" and sharing ideas, all in an attempt to learn.
To specifically address your question ...
...what could these divers have reasonably done differently, after they realized the boat was gone? ...
I will share information from the perspective of a professional rescuer who has been involved for searches for missing divers.
The first priority should be to establish positive buoyancy. Drop the lead! If you are cheap, remove the lead from the webbing/pockets and save the belt but do what it takes to get positive on the surface so you can stay on the surface.
I am a strong believer in trying to save yourself. If you are in good shape and are confident in your ability I am a proponent for trying to swim to shore, swim to buoys (navigational or trap buoys ... hold on to and prevent drift), or swim towards an area where you know boat traffic is common (towards a channel, inlet, popular reef, etc). These are risk/benefit decisions that are "owned" by the diver making them. I don't believe anyone is entitled to question these decisions because no one else is in your shoes (or fins) at the point in time these decisions have to be made. It is necessary to make a good decision though!
IF you believe there is NO POSSIBLE WAY to reach shore, buoys, channels, or reefs, then conserving energy and waiting is the only other option.
It is a fact that the victim can see search vessels and aircraft more easily than the searchers can see the victim. (As a person operating a search boat, I have NEVER been able to sneak up on a victim in the water and surprise him.) The goal of the victim when he sees an aircraft or a vessel is to make himself visible. Bobbing in the water waiting doesn't cut it at this point. The victim needs to become BIG for aircraft and TALL for boats.
To become BIG for aircraft, consider being horizontal on the surface and making the water white around you by splashing and aerating as much water as possible. The goal is to have contrasting color in the water. White water (splashing) on a blue sea can be a good contrast unless there are whitecaps, then you are likely wasting energy. Consider having the air nearly drained from your SCUBA cylinder and removed from the BC so it can float beside you. Because of contrasting color the tank can also assist in drawing attention to yourself it can be beneficial. Consider what clothing can assist in making a contrasting color. If you are stranded and wearing a black wetsuit, consider the risks and benefits of wearing it inside out so the plush fabric of contrasting color will be visible. Consider the risk and benefits of removing undergarments (t-shirt, swimsuit, etc) and placing them on the outside of your wetsuit. I have NEVER seen it done but if I was in the position of needing rescue, I would give it strong consideration! A black wetsuit or black dive skin just doesn't stand out when searchers overhead are looking into dark blue waters.
I can't stress enough how critical it is for divers to try to contrast themselves. (You might be regretting the purchase of that black BC by this point)
If the diver is trying to attract the attention of a boat, he needs to become TALL in the water. The "safety sausage" / Surface Marker Buoy does this well and I own one myself. It is cheap insurance that can pay huge dividends. Assuming you left it on the dive boat, try holding your fins above your head. Try splashing water into the air. If the vessel is close and they still don't see you, that is when the whistle might work.
On one occasion, I searched for a diver well offshore and did't find him. He was wearing a black wetsuit and a mostly black BC. He was found by a fishing vessel the following morning and stated that on multiple occasions search aircraft flew close enough that he believed he should have been seen. Additionally he stated that he could see search vessels and they were close enough for him to hear the outboard engines running. The victim swam continuously through the night working himself back towards the mouth of the Sebastian Inlet (FL). I credit him for putting himself in the path commonly traveled by vessels, even though he probably did it unintentionally. The victim's primary goal was trying to head towards shore and he may have made it on his own had he not been found. The victim was located approximately 12 miles down current and inshore from the last seen point.
On another incident, the victim stated that search crews were not close and he focused on swimming to shore. It took him almost 14 hours to reach shore. We know from his starting depth that he would have been about 10 miles offshore but there is no way to determine how far down current he swam because of a poor last seen point. The boat he was diving from was not equipped with a GPS or VHF radio and the inexperienced boat operator returned to shore to raise the alarm. The operator could not provide much information to assist the search effort. He could not recall times, did not recognize landmarks, and the only thing we had to go on was a general direction and a depth contour (assuming he could read the fish finder correctly).
Strobes and flashlights are obvious choices for divers lost at night, but in reality, many agencies will cease search operations at night. The exception is if there is good cause to continue; i.e., the family says the diver is equipped with an SOS strobe.
Obviously the best incidents are the ones where victims are found safe and have either made themselves BIG or TALL. If the diver can contrast himself, and if good information regarding the last seen point can be provided to search crews, the odds of being saved are much greater. It certainly helps if the crew on the boat is competent too!
Before I deploy divers, or before I go into the water myself, I typically set a waypoint at the dive entry point and set the GPS up to navigate back to the waypoint. I also typically dive dragging a surface float (dive flag) so the topside personnel can monitor where divers are in relationship to the vessel. In my opinion, the idea of having a boat follow bubbles is a disaster waiting to happen (though I give an exception to dive boats with an attentive crew topside and multiple divers staying together in a group underwater, following a pre-determined dive plan). The inexperienced boat operator I referenced above was supposed to follow bubbles and I can think of nearly a dozen other incients where divers were lost becasue the boats was supposed to follow bubbles.
RECAPPING; I am a proponent of PREVENTION and saving yourself. Buy a "safety sausage" or SMB if you haven't already and don't dive with idiots!
