Right, stopping the boat immediately is essential. Keeping your eye on the swimmer is essential, too. Broaching might do it if conditions are relatively light, and if they are, I think that's exactly what I'd do. But afterward the boat and helmsman (now solo) has to be in a position to assist, and probably, sail back to the MOB. So that means being under control. If conditions are boisterous, I think broaching with the kite up would have some ugly consequences. I'm thinking instead, first let the spin halyard run free. Leave the guy and sheet as they are (no time to mess with them), immediately let the halyard run free (out of the mast, no stopper knots in spin halyards, halyard flaked perfectly), and then turn upwind hard, stopping the boat and spotting the swimmer. You could do this in less than 20 sec even if you had to engage the autopilot first to free the halyard. Now you can reasonably get back into control, free the guy and sheet if necessary, leave the kite in the water, and sail back to the MOB.
Actually, some years ago while returning into the bay DH, under spinnaker in a big breeze, surfing wildly, with my crew at the helm unfortunately, we hit a wave from one of those Red and White Fleet tourist boats and rounded the boat down, hard. The mast hit the water and we were both thrown out of the boat. The interesting thing is that the boat stopped instantaneously, totally dead in the water and pinned down. Of course water was up over the coamings, so I was able to scramble back into (almost swim back into) the cockpit with relative ease, and then drag my crew back into the cockpit as well. Because the boat stayed pinned right down and water was dangerously close to entering the cabin, the 2 of us frantically tried to free the halyard, sheet and guy all at the same time... anything to get the kite free of the wind. The halyard somehow had wrapped around the masthead so it wouldn't budge. The sheets thankfully did run free. The boat righted, and the spinnaker, complete with sheets still attached, then flew horizonally from the masthead in the big breeze... in a singularly narrow, very long stream. It has to be the most exciting, and embarrassing, bay entrance I've ever endured.
Paul/Culebra