Big Blue Tenor Sax

Check out Bennie Wallace. "Someone to Watch Over Me" and "Moodsville" will fit your description nicely.

Gene Ammons, Stanley Turrentine, Illinois Jacquet, Ben Weber, Lester Young. As far as the recordings quality, sometimes it's the music that reigns supreme. Illinois has recorded some on Analogue Audio and that sounds great. Old CTI for Stanley. Ben on Verve. Good luck as these players all have the BIG tenor sound.

Right up this alley is most of Ike Quebec's old Blue Note catalog. Check out "Blue & Sentimental" or "Heavy Soul" Both are great, clean sounding recordings. Though older, they both sound as if they were recorded yesterday. Something more current would be Houston Person's, "Just Between Friends", a duo with Ron Carter, with a big slow sound, exquisitely recorded. Something different to listen to is Joe Henderson's "State of the Tenor" with bassist Ron Carter and drummer Al Foster. I prefer vol 2, but the 2 disc CD set has both volumes. Have a listen to the cut "Soulville". I also can add a vote for Celtic66's suggestions of I. Jacquet and B. Webster. Again, though older recordings, they typically sound great and both have that big slow sound you describe.

Ben Websters Soulville

You can get older higher quality recordings. Art Pepper has 7 albums out on SACD, all of which sound excellent. Never mind he is also a superb player, offering plenty slow ballads to boot.