Great idea, similar to my latch which also reuses the existing screw holes in the front opening of the fridge.
The difference with mine it is a slide latch that stays on the fridge between the two doors.
Went to Home Depot and searched for a slide latch the was small enough to fit between the doors then made some shims and a bracket to get the position just right.
latch view
1
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Latch view 2
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Latch view 3
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Latch view 4
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Note, the pop up button is to prevent the slide from moving while traveling. That button was part of an defunct electronic gizmo that was a spring loaded contact. Most likely not needed but I was making sure the doors would not pop open while traveling!
Somewhere if I can find it I have a picture of the latch on the fridge.. but right now I am not sure what folder it is in..