How wide is the gap. If it is real narrow you might weep thin Cyanoacrylate glue into the crack. Shoot, let dry, repeat shooting CA glue into it until no more will suck into the crack and you build a little mound to be filed or sanded off after. Shoot it into both sides. The ca glue will weep into every nook and cranny and small fissure by capillary action and seal & fill. I've used thicker ca glue on bigger gaps and fissures also but the gap would have to be shallow because the thicker doesnt capillary as well. I learned that trick in the Guitar repair business. I've glued guitar headstock fractures (you want to talk about string tension there - 6 metal strings) and neck fractures that way without having to break the fracture apart. I had one come back broke a second time (1" away from the last repair) and the old crack held. makes an almost invisible joint. fills tiny areas in joint lines that suck laquer finish into them (just like it does to the ca glue) and show in the finish. couple of spots of ca glue on top of the laquer finish, sand flush and re-laquer - no more sucking into the joint.
You got nothin to loose trying it (unless the gap is half the length of your bow
). Sounds like a lot more work than it's worth trying to saw it apart with all the joint work getting it to mate good a second time.