This is sort of uncharted territory, so I am just spitballing here...
It's probably more important to inundate the crack with glue than it is to have the glue be strong. I would want it to be more viscous than superglue, and have longer set time. So...some alternatives...
You could use epoxy. That would give you more set time and be even stronger than superglue.
You could use a hard polyurethane glue. The good thing about that is that it will expand as it cures to fill the space. It's not usually recommended for guitars because, sort of like epoxy, what you glue with it will not come unstuck. Bad for necks, but maybe OK for this.
If it were me, I would probably use something like an aliphatic resin or hide glue with a syringe. I would want to thin it enough so that I could shoot it way down into the crack with the syringe. Tite bond can be thinned up to 5% with water. If that's not enough, I'd look for one that could get thinner. Hide glue gets thinner by heating so you'd want to syringe that isn't bothered by heat. Once the crack is innundated with glue, I'd clamp the body. tight enough to get squeeze out from the crack. You could clamp big clamps...but if you don't have enough nylon cargo straps or even bicycle innertubes can be used to do the clamping.
Since I have not tried any of these approaches with a crack, I am hoping others will chime in!