I've been using an Ortlieb with the map attachment for years. It is possible to get the mounting cable snug but not so tight that it gets damaged. If it is tightened too much, you can buy a replacement cable or mount. I've done all three (reused as is, new cable, new mount).
The Ortlieb is a nice bag, a bit on the large side, so make sure you fill it with fluffy things that don't weigh too much. It's seriously waterproof in hard rain, at least until you open it. That "troublesome" mount is secure and stable, and it will give you no trouble once it's on until you need to change your bars, whether that's from an accident or replacing a broken frame. The map holder may flap a bit in a headwind over 20 mph, so I supplemented it with 3' of 1/8" shock cord looped around the mount that I can stretch over the map holder to keep it secure.
Arkel also has a nice bar bag with map holder, but I don't have any experience using it.