The Big Al track is the title track to the Three Sounds Beautiful Friendship LP. I knew @Dan Gould would quickly identify it but I'm still tickled he didn't immediately ID it. Mission accomplished.
To re-iterate my reasons for selecting this track:
Awhile back I was trying to build a discogs cart to the seller's minimum order and this was listed for very cheap. I like the 3 Sounds and I like how much fun those Limelight record covers are. Ended up enjoying the record more than I expected simply because I wasn't expecting a big-band record. A very enjoyable record.
When Dan announced this BFT, selecting something from this album was a no-brainer as a simple tribute to the former Gene Harris Fanatic. I kinda figured he had this record, but this felt obscure enough to fool everyone else. Which, apparently, it did. As @tkeith said, "Big Al FTW!"