Personally I’d put a wedge in to very slightly ease open the crack & then use a dremel or similar to remove wood from the inside of the stock, ie open up the gap slightly, but leave the outside & both edges untouched as these will be the edges of the jigsaw that’ll make sure the stock is aligned correctly later.
Then remove the wedge & use surgical rubber tubing to wrap the stock to make sure the joint is tight before drilling a couple of holes at an angle through the crack so it can be dowelled later.
Keep the saw dust from these holes for use later.
Take a bamboo barbecue skewer & sand down to the right size to fit the holes & cut to a length that is slightly shorter than the depth of the hole. Bamboo is flexible & has a course fibre structure so very unlikely to shear but will flex if required.
Make sure you’ve cleaned out all the material you’ve removed by using compressed air (available in cans).
Open the crack up again with the wedge & use a good epoxy glue to fill the gap, including he wider bit you’ve removed the material from. You can tape off the wood either side of the crack to stop the glue going where it shouldn’t & cling film works well to cover the rest of the stock so you don’t leave sticky marks!
Put epoxy into the dowel holes too & then remove the wedge before using the surgical rubber tube to tighten the crack up. Then insert the dowels & push them to below surface level. Mix the sawdust you saved with the remaining epoxy & use it to fill the dowel holes.
Once the epoxy has gone off a bit use a razor blade to trim back the epoxy on the dowel holes.
Once it’s all gone off remove the surgical rubber, clean up the inside with the dremel to remove glues that’s squeezed out & clean up the dowel holes.
You should be good to go & as others have said, the repair will likely be stronger than the stock!