I don't have a GHB (mostly because, I work from home 80% of the time!)

But I did have a somewhat similar setup to what you describe on a trip I recently made. I had my suitcase (carry on) that was full of clothes and things I would only be using in the hotel. And inside that suitcase, I had an EDC bag. The EDC bag contained things I use when outside of the hotel - on day excursions (examples: binoculars, water bottle). For the things that I might be using EITHER on a day trip OR in the hotel (examples: Tylenol, Android tablet, flashlight) - those things resided in the EDC bag.

There were a lot more individual items in my EDC bag than in my suitcase. But the EDC items were smaller in size, so they fit easily in the EDC bag. My suitcase was big enough to hold it's normal stuff (mostly clothes) and also had enough extra room for me to put in and take out the smaller EDC bag.

My suitcase was serving a similar purpose as your GHB. It contained items that would be needed at some point, but not as often as the EDC items. I left my suitcase in the hotel. You'd be leaving your GHB in your car. You EDC does not necessary have to fit inside your GHB as my EDC fit into my suitcase. Your EDC would be perfectly OK if it attached to the outside of your GHB, maybe using molle attachments.

You're not using your EDC -or- your GHB. You're using your EDC -or- your GHB/EDC together.