Try to rely on AC's MainCamera for your rendering. You can still use a custom camera, but have AC attach the MainCamera to it like it does any other GameCamera via Actions / Scene Manager. Attaching the "_Camera" component to it will enable AC's various UI fields to make use of it.
I am using ACs main camera for rendering. My actual "camera" is untagged and has an AC script on it (can't quite remember which) to move the MainCamera around with it.
I think I deleted the MainCamera while trying to get the custom controller to work with AC and had to recreate it so maybe I did that wrong? Is there a Prefab I can use to recreate it?
I just realised I didn't have my camera put into the default in my scene settings but when I do it tells me "main camera doesn't have a main camera component" when it does. Doesn't change the sound situation though.
Have you removed the Audio Listener component from your custom camera? Unity only allows for one in the scene, and the MainCamera should already have one.
Actually it still doesn't work until I press ESC unless I have "maximise on play" selected. So hopefully that means it will work when it's playing a build and just not in the editor.
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Going back to your deleted MainCamera, bring back the "proper" one by dragging in the prefab from /AdventureCreator/Prefabs/Automatic.
IIRC, the UFPS integration had a similar issue - which I fixed by running the following in the UltimateFPSIntegration script's Start() function:
AudioListener.pause = false;
Try adding that to your custom camera script.