I wonder if they really have that much music to clear. The show was extremely low-budget; they had Efrem Zimbalist walk along side a slanted bannister and gradually scrunch down just so they wouldn't have to build an actual staircase on the set. So, while they probably did use some songs that require clearance, I'd think that would be the exception rather than the rule. Why pay to use a tune when they had a full library of songs at their disposal? I found this on a site dedicated to the show:
Knowledgeable viewers will note that the Warner music catalogue was used extensively in the background of 77. Anyone familiar with the works of the Gershwins, Cole Porter and Rodgers and Hart will not only recognize their songs (controlled by Warner Records) in every episode, but if one knows the lyrics, they will note that the tunes chosen invariably make musical comments on the scenes in which they are played.
There a lot more interesting stuff about the show at this site
, including several fascinating interviews with Zimbalist and others, but you'll have to poke all over the place to find them. The linkage isn't very intuitive and some of them don't work as they should. I saw that a few Season 6 episodes showed up online so I watched a few minutes of one of them to remind me what they were like. I'm not surprised that audiences didn't take to such a radical reinvention. Instead of being at a fictional address on Sunset Strip, Bailey's office was now in the historic Bradbury Building on an upper floor, and he worked alone. Ironically this is closer to Roy Huggins's original conception, but it was too great an (unexplained) alteration from the previous five seasons. I have most of season five to finish before I start in on the Webb productions. I still want to see the five-part story that opened the season however (it's not yet listed online); I can still remember a few scenes from it. It might be considered the forerunner of the miniseries.