Funny how the weight adds up. Ditto on two tubes and another bungie. Back in my 20's when I rode a lot carrying two tubes became a habit for training because I didn't want to be stuck on the road looking for holes in drizzly cold weather waiting for the glue to dry or hoping the rubber was dry where the patch was going. Also there were those days when everything goes wrong, not often, and you get multiple punctures.
Did you try orienting the large bag lengthwise on the rack?