I have given this some thought over a nice glass of wine. I did limit myself to the year criteria, but I submit for your consideration:
Gene Ammons: Boss Tenor (1960) (possibly an exact match for what you are looking for)
Gerry Mulligan: Gerry Mulligan Meets Ben Webster (1959) (highly acclaimed session, lots of great relaxed sax, including baritone)
Duke Ellington: Duke Ellington & John Coltrane (1962) (not big band, just sax, piano, bass, and drums. beautifully introspective)
Zoot Sims: Blues for Two with Joe Pass (no drums but a lot relaxed breathy sax and guitar interplay) (1982)
Dexter Gordon: Ballads (1960s)
These are slightly more uptempo:
Paul Desmond: Two Of A Mind (with Gerry Mulligan and Jim Hall)
Sonny Rollins: Saxophone Colossus (1950s) (a classic and very tuneful)
Stan Getz: Jazz Samba (great sax, and with Charlie Byrd on Guitar I dont think you can go wrong).
Have Fun!