Two songs on the 'underachievers' list which just popped into my head are The Girl I Never Loved from Clambake (underrated soundtrack IMO, despite Confidence) and So Close, Yet So Far from Harum Scarum. A couple of great love songs which are both rather unique, I think.
Although this one may not be generally overlooked or dismissed, I still don't think people appreciate it as much as it deserves, so I'm gonna mention it: the Today, Tomorrow, And Forever duet released just 3 years ago. I think it's incredible...just a beautiful 'declaration of love' type of song given an affecting, immaculate delivery by both participants.
Back to P,HS...You know what's funny about its inclusion on the Aloha special and how, if you didn't know the song from the movie, you'd assume he sung it then in '73, 7 years after he actually had? To me it's odd because if he had sung that song on the Comeback Special, at the American Sessions, or even around the time of TTWII and a little beyond, and they used it in the special, it wouldn't have matched half as well vocally. That sound he had in '66 he only had for a relatively short while, but after going through a few changes, it basically came back to him later.