This is more a CC+Burn style of gameplay. Big engages with your ultimate (You can use Athene's along with Frozen heart if you need it more often (But 1 ace at a time should be enough after laning phase).
The key here is to keep them under control, get in, and get out if it's too much. There is potentially approx 10% current health per second to everyone around you. Given your stun, along with Zhonya's, and say half a second for reaction time between the two, that gives you about 5s of damage. That should take anyone that sticks around through the Zhonya's down to close to 50% health by yourself; not including team damage.
Also great for those champs that try to get away, the slows and aoe health burn will make the chase last only a few seconds.

The downside is anyone that doesn't get caught in your initial stun (though bandage toss should keep them still), or anyone that runs away while you Zhonya's. The upside to them running away is that it should at least give you a gap to escape through unless they have gap closers.

Sweeping lens and bandage toss for solo dragon kills from level 5/6 - requiring Cinderhulk at the very least.