A problem with putting epoxy in there is the adhesive will flow into the fibers of the the wood, possibly too much. This is one of the problems with epoxy and clamping pressure, Its easier to starve a glue joint with epoxy.
Wood glue is able to glue the same kind of joint with less than epoxy for a similar joint, i.e. a tight joint. The problem gets worse with epoxy that cures slow because with longer glue time, the epoxy can flow for a longer time away from the joint into the wood fibers.
I would recommend now that you have the crack glued is to inlet a couple dominoes into the grip. If you have a mill, inlet a pocket on either side grip. If you don't have a mill, you can make a jig and use a router but it will be a little involved.
You can use an internal piece with a shape that can hold the crack like a bow tie shape and then an outer domino to fill the inlet. You can use epoxy internally but I would use wood glue for the edges of the outer piece because then you can fit the piece very tight. With wood glue you don't really even need space but with epoxy if you don't leave a gap, you won't be able to fit any glue in.
There is difficulty in getting glue all around a dowel when you put one in the wrist. It's stronger with the dowel. If I wanted strength I'd mill all the way through and put a piece of good plywood in the center and then match the wood on the outside.
Because you got if for a song, youre probably not so worried about hiding it but if you want to hide the patch, stipple the grip and put a little dark finish over the stippling.