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.
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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.
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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.