A standalone map case like the Sea to Summit is my fallback option.
I have a couple different ones I use backpacking. The ones I have are too large for this application, and the vinyl thick enough that they don't fold well. (Normally I would roll them and stick them down the side of a backpack.) The small size Sea to Summit looks like a better size.
I had been thinking that I may DIY something with some Velcro Onewrap, a binder clip or two, and an appropriately sized Aloksak. I think I recall Aloksak having a bag with internal dimensions of ~8.5" x ~5.5" (e.g., a standard US letter sheet folded in half). That's probably the best starting point. But, as djb suggested, I'm not sure what the best attachment options are going to be to minimize both flapping and the loss of hand positions. I've only had this new bike with the Jones bars for about 10 days, so I'm not yet sure which of the myriad hand positions I really care about (I like the bars a lot so far, though).
I'm hoping someone more experienced will hop in with an elegant solution. Short of that, the answer will probably be just to throw some extra Velcro and binder clips in a pannier and figure it out on the road.