If you can get one cheap, replace it. Otherwise, I'd work out the clamping needed (some kind of jig I suspect will be needed), then use Titebond III so it stays open for a bit as you clamp the pieces so that the joint disappears.
The way that sheared, the stress is the recoil going straight back. So I think a brass or even steel bar should go through lengthwise, not across the new joint. Once glued, I'd let it cure for 24 hours, then consider drilling for a 1/4 inch rod. I have some very long bits that would probably reach through the stock, and you can always drill from the the front of the repaired stock. I would consider using epoxy for the long pin. Epoxy has a way of expanding that makes it a poor choice for piecing the stock together. Titebond doesn't do that. if you want to rebalance the stock, drill for a heavier, shorter rod on the front grip, plug the opening and refinish to make it invisible.
You might have to refinish the joint a bit, maybe a little careful sanding, to make the edges of the joint disppear. You will want a little squeeze out to be certain the entire split is covered in glue.
The more I do, the less I accomplish.