I run ozone with an ASM G-2. I used to run carbon, and I know that it is most likely safer to do so, but I've been running it for a long time without it and have never noticed a difference. Ozone is very very unstable and breaks down very quickly on its own, with little chance of actually reaching the display tank.
But when I ran carbon, I did it by putting the carbon actually inside the skimmer return pipe. I didnt put it in the collection cup, because I figured that to be pointless since the ASM skimmer is not open on the top. Hope that helped.