What's the counterplay against Zz'Rot/Banner comp?

Basically, everyone builds a ton of waveclear ( and either or ), take teleport, and splitpush all game, trying to avoid teamfights. Zz'Rot, Banner, and Sunfire are pretty self explanatory. Ruby Sightstone reduces item cooldowns by 20%, so Zz'Rot and Banner come up more frequently. Boots of Lucidity lower the cooldown on Teleport further. Bot lane can take double relic shield to sustain through the early game.

We won the two games, and won them hard. We had full map control almost all the time, and they couldn't push. http://matchhistory.na.leagueoflegends.com/en/#match-details/NA1/2386682291/216352813?tab=overview http://matchhistory.na.leagueoflegends.com/en/#match-details/NA1/2386557687/216352813?tab=overview

That said, these were low elo games. Which is why I ask, what's the counterplay? The traditional way to counter splitpushes are teamfighting as a larger group, but that doesn't work against this.

Teamfighting and pushing as a group doesn't work because they can't outpush the portals, and pushing against a Zz'Rot is also hellish. They can't catch people off one by one, because of Ruby Sighstone's vision. For one push, we put wards around the entire red side of the enemy jungle. The splitpushers are also very tanky from their builds, so it's difficult to kill them. It's also difficult to just turtle and defend, because Banner minions are immune to magic damage, and Zz'Rot minions spawn every 4 seconds. This also leaves other objectives open.