My usual search engine doesn't search when I put in Hoagy Carmichael - it just goes straight to Hoagy.
Back when I was playing dance bands in prehistoric days, it was nearly impossible to find any H.C. songs in the fake books. Even attempts to buy them as individual issues was seldom successful. We were always told that it was because of extremely tight copyrights.
Copyright dates shown at the site above would seem to indicate that many are now "p.d.," but they may have just been out of open circulation for so long that there are few sources available(?).
Fake books I've picked up in the last few years still show "copyright renewed" notices on most of the Hoagy songs.