I don't see how this situation is different from an MTB with a flat bar.
If you look at this Revelate SweetRoll you will see it uses stackable spacers to gain clearance for the levers.
![](https://www.revelatedesigns.com/layouts/revelate/files/store/productphotos/35c4a98d-24f0-4af6-b5b8-4ec7b6ae3ed7.jpg)
You can easily make your own spacers from rubber tubing, for example short lengths of car radiator or heater hose with a large enough inside diameter to pass the webbing through.
Another option would be to use a
Revelate Harness or a
Specialized Burra Handlebar Stabilizer Harness with a drybag.
![](https://www.bike24.com/i/p/7/3/131037_00_d.jpg)
![](http://cdn.bikepacking.com/wordpress/wp-content/uploads/2016/07/specialized-burra-burra-handlebar-harness_wh-02.jpg)
It's also fairly common practice to lengthen and/or re-route control cables to clear the bag. Google Images has many examples of handlebar bags for your inspiration.