Very well, thanks a lot for your advice. I will try it without AdAdway.
I currently have only one app that shows ads (Easy Currency), and it still does it despite of AdAway being up and running, so I assume AdAway is not of much use for blocking ads in apps because they are fed in a different way.
For most users Bromite itself will be sufficient; I see you are also using the SystemWebView, so I don't think you need to run AdAway, you can save CPU usage and battery without it. I suggest you try disabling/uninstalling it, there should be no difference in your experience.