The ACA has some options. The Arkel small and large handlebar bags both come with a map case and don't exceed 13" in any direction.

You might instead opt for a regular map case and a separate bag without map case. When I was using my Topeak Tourguide Plus DX handlebar bag I found it hard to look at the map while riding since it's on the opposite side of the handlebars. The map case by itself goes in front over the stem and is much easier to read while riding IMO since it's right in front of you.

This link is to the ACA Cyclesourse store where you can find all 3 of the products I mentioned...
https://www.adventurecycling.org/cyc...words=map+case