I think pull it off, slightly pry apart at crack and insert glue or slightly thinned epoxy into the split, let that dry/cure (clamping to hold proper position?). That'd probably hold well enough if you got a good coverage inside the split, but you might as well go all out... -> Once dried/cured, go for dowel insertion from the bottom. It's closer from there (so less drilling/dowel length needed), and will be 'hidden' when done, and that means a bonus - water will find it harder to get into.

Looks like some water got in already, so you might want to allot some drying time pre-repair. May be that removing some of the finish around the 'wound' will speed drying.