"Group of six" and "f/2.8" go together like bathtubs and electric radios, like Jack Daniels and speedboating, like loaded guns and moonshine whiskey.
I'm not trying to be flippant...f/2.8 and group photos with anything with a sensor bigger than a smartphone sensor is just asking for issues. It really,really is.
But yeah...you have the right idea with the 24-70mm zoom, to stop down to f/5 or f/5.6, and make the shots at that much safer aperture.
The thing is that with six people, there's a good chance that one,two, or even three of the people will have their faces at significantly different distances from the central face in the middle of the image area. If you actually take a steel tape, and measure straight ahead, from 12 feet, and then at the edges of the group, framed from 24mm to 40mm, the diagonal distance to the people at the edges of the picture area will be longer than it is to the central people; longer to a degree that will put those outside faces behind the plane of sharpest focus. An this is considering that everybody's toes are on a straight line! If one or two or three of the people are separated by eight to 10, or 12 inches, or as much as 18 inches, you will have a definite focusing problem, easily visible.
If you moved the camera back a good number of feet, yes, you'd get deeper DOF, and you could probably shoot at f/2.8 and pull adequate focus. But still...f/2.8 is very critical...it offers very little margin for error, and does not allow a lot of flexibility for loosely posing groups where people are at slightly different distances.