This is the deck I've wound up with tweaking the Apex Hyperdriver deck that was posted from the King of Servers tournament. I'm not going to argue that this is stronger (it isn't), but it does have the "what ARE you doing?" factor, and the most janktastic "breaker suite" I've ever cobbled together!
There are four main things that Ice does and this deck has a counter to all of them*:
End the Run -> Endless Hunger
Trash a Program -> Sharpshooter/Clone Chip
Do X net/meat/brain damage -> Heartbeat
Give the runner X tag(s) -> Dorm Computer
"Wait, what?! Dorm Computer!?" I hear you saying; "Really?"
Yes, really. Dorm Computer works so well in Apex; It turns off many pieces of NBN Ice entirely (especially during those critical Apocalypse runs); It combos with Heartbeat to take the rest of the sting out of Snare and Ichi's 3rd sub; and if that wasn't enough, it hangs around when empty as Power Shutdown protection or fodder for Endless Hunger and Heartbeat.
*Yes, there are many other niche things that Ice can do, and some of them will give this deck fits (I'm thinking of Wotan, Wormhole, Orion, and Draco particularly). You can't plan for everything.