Honestly, after dealing with this exact issue I just stopped carrying my own headset. At my shop, *most* of the guys who carry Bose and CA carry the case on a carabiner attached to some part of the rolling kit. Me? I just use the ship headsets because they're all new. I carry a little pouch of mic muffs and o-rings, and Tech Ops will bring them to the plane if you ask nicely, so it works out easier.
I've actually resigned myself to 2 different bags and it largely depends on the trip and how much I'll need to eat. Since I'm on long call this month, the Brightline is getting used more, since I only pack 1-2 meals in it that I know are going to defrost over time. That amount of time and the trip are what determine it. Longer than a 1-2 day, or something where I don't overnight in DCA, and I'm loading the Strongbags cooler with food and transferring major items (flashlight, shaker bottle, spare eyeglasses, sleep buds, grip strength gadgets, pre-mixed protein shakes) from one to the other. All the little stuff (first aid meds, pens, lanyards, phone chargers, various and sundry bits) exist in both bags all the time.
This is the system that is working out for me. When I hold a line again next month (praise be) I'll alter the equation slightly.