U of SC Honors app was 5 essays as recently as 2 years ago, if that’s any consolation. They requested apps by 10/15, I think, so make sure they’re still accepting Honors College apps before you knock yourself out on the essays.
Still not sure that you understand that merit aid usually replaces (is not in addition to) need-based aid. If Case Western or Tulane offers you $30,000 per year in merit, they won’t also offer you need-based aid, as your cost after merit would be less than your EFC. So your annual cost will be about $36,000 at CWRU, closer to $40,000 at Tulane.
Duke offers a very few high value merit awards. They don’t offer $10,000 merit awards to random applicants. And you say you are award that Yale offers zero merit. So we don’t understand how, if the NPC at those two schools shows a price of $40,000, you hope to get merit to subsidize another $10,000.