Lazy's solution has my vote.
If you can press the pieces together and get a good fit, you can avoid the slight amount of reshaping the edge that planing would entail.
Planing will take you back to 100%. Re-gluing will get you close. If you re-glue, I'd add some biscuits or dowels to reinforce the joint.
Definitely remove the glue from the underside where the battens attach and do the slotted hole technique recommended. That is likely why the crack developed in the first place.