Very sorry it didn't make it but I think you did everything you could to help it. Unfortunately sometimes they have internal problems that we can't see or diagnose.
Do you know how to pry open the beak with a finger? It may help to have someone else hold it securely while you do that with one hand, and other hand can administer the Nutri-Drench.
I don't really measure amounts, but since it's a little chick, maybe 0.1-0.2 mL at most in a session. Try a...
Buy a plastic syringe or an eyedropper and drip it into its mouth. Just be careful because chickens can aspirate easily, so never try to force them to drink, but if you drip it onto the lower beak the chick should be able to swallow droplets like that.
Not sure about the yolk but I'd direct dose with undiluted Nutri-Drench maybe twice a day for now. About 10-15 min after dosing offer it some food and see if it'll start eating on it's own.
What kind of vitamins are you adding to the water? If you don't already have some, I would recommend Poultry Nutri-Drench, which has some vitamins and molasses to help perk up birds that are lethargic.