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Well, if it's glued to a base even if the crack did finish all the way through the stone it won't effect honing anymore than it does now. With both pieces stable relative to one another and lapped...

Wood is probably do-able if it's coated with a nice water resistant polyurethane sealer. Which is also what I used to seal the sides and bottom of my Jnat. So I was thinking glue to backer, coat both...

You could consider sealing it. In this case I would probably sacrifice the ability to use the back of the hone and glue it to a wood base too. It's easy to say 'just replace it cause they're cheap'...