For added strength (you don't want to have it break again!), you could consider sawing as you mention, then making two evenly spaced longitudinal cuts across both sawn surfaces, and gluing in splines with the grain traversing the oringinal cut. If you're very careful about lining everything up perfectly, it should come out okay, maybe a little trimming/sanding. I think carpenter's (yellow) glue would probably be appropriate, since, hopefully, no-one will have to re-visit this one!
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