I think it makes sense for a general "greek hero" subclass to be a paladin, as they're strong and charismatic, but the features don't emulate Greek heroes as much. Heracles was strong, which the first Channel Divinity shows in mechanics, as well as making you better at jumping, which is also accurate. The thing I don't like about the second channel divinity is that no greek heroes have anything similar to this. You don't smite someone with divine power and heal other people in greek myths. You can smite people with divine power harder than anyone else, though, which is why I preferred the UA version of this specific Channel Divinity.
The aura also seems weird. Greek heroes are fast, but they don't make other people fast.
The last two abilities of the paladin I'm fine with, they feel hero-esque.