Three out of the four Elephant units that we have in AND are double-teched. This is what I think we should do with them.
Elephant Rider: Currently requires Horseback Riding and Warfare. This is one of the very rare cases where I don't think it's a good idea to drop either tech. If we drop Horseback Riding we lose a serious level of verisimilitude. I'm not a super-stickler for realism, but it does need to feel plausible, and riding Elephants without Horses loses that. Without Warfare, I am afraid that Elephant Riders would show up too early and be too difficult to defeat on the battlefield, especially as it is longer to get to Bronze Working and Spearmen than Horseback Riding. HBR just requires Agriculture/Hunting -> AH -> HBR. Bronze Working requires Agriculture + Stone Tools -> Crafting and Mining -> Bronze Working.
Also, Elephant Rider has +25% City Attack that I don't think it needs. Elephant Rider's 6 Strength is better than just about anything else at this point and I don't want taking early cities to be easy.
War Elephant: Currently requires Construction and Horseback Riding, exactly the same as in BTS. I actually think it would be a good idea to swap the War Elephant over to Stirrup to match the Heavy Horseman.
To slightly clean up the War Elephant, I also think it should have base Strength 9, no bonus at Mechanics, and at least +3 Strength at Siegecraft. This way it starts off slightly stronger, then is not as strong as it used to be in the late Classical, then returns to its previous strength in the Medieval.
Elephant Bombardier: Currently requires Chivalry and Gunpowder. With the new requirement of Stirrup for Feudalism, Chivalry isn't as necessary. Before, you could get to Gunpowder without even Animal Husbandry. Now you can't. So dropping Chivalry is easy enough.