Mark, thank you for sharing this treasure.
I don't agree about his songs lacking memorable organic melodic meaning, but one I think you'd find has it is "Good Thing Going," from Merrily We Roll Along. Sinatra covered it (on his She Shot Me Down album), and it's one of the best Sinatra performances from his later period. Another Sondheim song I bet you'd agree has a strong melody--that might be the best Irving Berlin song Irving Berlin never wrote--is "The Best Thing That Has Happened," from his last show, Bounce.
His main complaint with Hart was not Hart's cleverness per se, but the way he would write un-colloquially for the sake of a rhyme. (Wrenching around word order to antiquated forms, for example.) For Sondheim, if a character ought to sing un-colloquially (if the character were a highly educated academic, for example), that's how you should write lyrics for him, but if the character is a regular Joe or Jane, you find a way (without sacrificing strict rhyming) that sounds like something they might actually say, or sing.