What about using an overlap on the two stiles instead of the current design ? Overlap could be routed into the two stiles ( vertical piece of the frame) where they close together or as an applied molding extending past the closure edge on one of the doors. With the overlap, you can cut back enough of the stile to allow for expansion and still give the appearance of tight closure.
Otherwise, with wood, you need to maintain a coating to reduce moisture level changes in the wood that causes the expansion.
Are the doors exposed to direct sun and rain ?