I usually bring at least one skink unit with a brave when I have an EotG.
I put the EotG in the skink unit, using the speed of the skinks to my advantage to get the charge on something (impact hits) After that, you can do conflagration (more damage) and combat.
In your opponents turn, he'll probably challenge. Accept with the brave. You're stubborn because of the steg so overkill doesn't matter.
Next turn you do conflagration and combat again.
His turn, he'll probably challenge again and kill your priest. No biggy, because if your priest is killed, the stegadon must be removed from the unit because he is no longer a ridden monster.
Only problem that could arise now is that the skinks break, but when you have a general and/or a BSB nearby, you should make it.
Next turn, you can charge with the stegadon again! More impact hits!
Now I haven't done the mathhammer on this, but I'm thinking that there aren't a lot of units that can take this kind of punishment. Put some krox in the skink unit if you're afraid of losing too much combat res when the steg is forced out of the unit.
Please tell me if I missed something obvious.
Kajchi