I am having success against AP Ezreal using champions who are capable of pushing the lane hard early

and without losing too much mana (or without even using mana, for that matter)

Everytime the enemy picks Ez, I pick champions such as (can push the lane without eating too much mana thanks to his E) (doesn't even have mana) and (his passive can recover mana)

The reason for that is because while AP Ez can solve his waveclear problems with Runeglaive, he obviously can't have this item during level 1. So an AP Ez with Smite is essentially the same as an AP Ez with Ignite/Barrier, he just has an spell that is useless for laning. He still has horrible waveclear. Pushing him hard can work well, and if you ward properly and plays correctly, ganks should not be a problem.

That's why I like to use Malzahar against AP Ez; he can push the lane without going OOM and doesn't have to actually sit on Ez' tower to push, he can stay at a safe distance to avoid ganks. Also, Malzahar has his ult, Nether Grasp, to suppress Ezreal during situations such as teamfights, making him a non-threat unless he purchases Quicksilver Sash, which is an item that AP Ez definitively can't afford to purchase before at least purchasing Runeglaive, and also makes him weaker overall because this item and its upgrade offer no AP at all.

However, I've found that Cho'Gath also works well due to his sustain, and because he is safer than Malzahar. He also has a more reliable silence and has a lot of CC. He won't just be bursted down like other AP mid laners, thanks to his natural tankyness.

Peharps can work too? He is the definition of pushing the lane hard, and Ez can't easily destroy his turrets. It is also extremely difficult to gank Heimer due to those turrets. However, I am not a Heimer player myself, I can't test if he would work well.

I am not saying that they are hard counters to Ez, but peharps picking a champion that can push the lane without eating too much mana can be a good choice against him?