This is actually exactly what they did that prompted my initial post last night.
It was a 2v2 and the other player went for Jaeger armor. It didn't help that the game was on Minsk where the Elephant can really dominate because of the lane design of the map.
Anyhow, I disagree that this ability is 'easy' to dodge, especially in 2v2 (which is all I play recently.) You can't afford to move ALL your units every time you hear the sound. We're seeing Jaeger armor in almost every game and I'm seeing this ability more and more. It's the Zis that tend to get targeted especially once I get vet on them. Even if you try and move it very often it still gets destroyed. Vehicles aren't as much of an issue, but with the elephant around the Zis are usually key to staying in the late game. Once they're gone it's that much easier for the elephant to dominate.
Agreed that the player with the elephant will target zis guns heavily and this can be very hard to dodge.
The doctrine is very good in the late game and it is designed this way.
I would try these steps:
1) Use an inf flank to cause the elephant to turn towards you. While doing this send in t34's on the other side (even on Minsk this is possible).
2) Get either the T34's up to the elephant or the inf, the elephant cannot fire on the move.
3) If you get inf, get as many at nades on the elephant as possible to get damaged a engine. If t34's block its retreat path and fire into its butt.
4) One of you should have some artillery, any kind. Use it to keep paks away from the t34's while they beat on the elephant. Kats work well for this, but you can rely on call ins as well.
5) If you fail don't give up, the damage you dealt is still on the unit. Use artillery to keep pinging away at the elephant and killing pio's trying to repair it. If you got an damaged engine it can only just creep backwards.
One of you should also have SU85's or heavy tanks so once the elephant tries to engage the t34's these should be brought to the front line immediately. They should have been sitting just out of range of the elephant.
Make it your mission while they are fighting to send a unit like penal squad in to kill munitions caches extremely quickly while all this is going on. You must stop the munitions flow. If you can drop him <40 it will take almost 5 minutes to get a stuka dive bomb. Not even close to how fast you can field zis guns, assuming he does not use munitions for anything else in which case you will easily outpace him.
Never ever clump high value units, or if you do make it seem like a juicy target and then move them quickly to draw the strike.