If It were my project, I'd probably tack (with hot glue) a nice wide guide strip (a 2-3" wide strip of 1/8 plywood?) to the deck and use a router to cut a new groove for that midline stripe. The smaller the router, the easier for that kind of job.

John, I do this all the time. It's easy to get a straight center line joint. Pictures from the 2008 "Nereida" Njord. Here I filled it in with the same wood as the field. I could have easily have added an accent stripe. The woods are Honduran Mahogany, curly maple and walnut. If the right pattern you can also inlay curved accents this way. Naturally, you want to keep the router tight to the guide strip. You can make a big mess, really quick.

In his case there's no reason to do a full thickness strip. A partial inlay as others have discussed would be more than adequate.

The pieces are roughly run to the center joint and then a straight edge is hot glued in place.

Chuck a spiral cutting bit (3/8" diameter in this case) with a bushing and route out the material.

Cut, fit and glue in the center piece.