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.
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.
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.