UPDATE: Links fixed - however, you may need to save them to play them for reasons I can't quite figure out.
Here are some recordings of acoustic chordal solos that I consider essential (and are easily linked to at Classic Jazz Guitar). Yeah, it's lame that these are just clips, but you should just go by the tunes now. Go on itunes or amazon.com and just buy all of them now. Go. I'll wait.
Allan Reuss - Beside being one of, if not the best swing rhythm guitar player, Reuss was also my favorite Block-Chord Soloist. The solo on "Bye Bye Blues" is amazing. Reuss had many gems on record through out the years.
Arnold Ross Quintet f/Benny Carter - Bye Bye Blues
Lionel Hampton - Rhythm, Rhythm
Jack Teagarden Orchestra - Pickin' for Patsy
Coleman Hawkins - Stuffy
Benny Goodman Orchestra - Rosetta
George Van Eps - Although he is now mostly famous for inventing and playing 7-string guitar, Van Eps was a fantastic 6-string rhythm and chordal player. He was a cooler player that Reuss, and he approached the guitar more like a "lap piano". Still, he had some great block-chord solos on record.
Adrian Rollini Orchestra - Somebody Loves Me
George Van Eps - Ain't Misbeavin'
Jess Stacy - Indiana
Carmen Mastren - Another great rhythm player, Mastren started out with Wingy Manone, but most famously he played with the Tommy Dorsey Orchestra and even did some arranging for the band. He later joined the Glenn Miller Army Air Force Band during World War II. Here are his two most famous block-chord solo breaks are with two one-off quartets.
Delta Four - Swingin' on that Famous Door
Bechet-Spanier Big Four - If I Could Be With You
Carl Kress - Kress' chordal style descended from extented Tenor Guitar / Banjo tuning. He famously recorded duets with Eddie Lang. After Lang's death in 1933, he partnered with Dick McDonough, until that guitarist's death in 1938. Kress also did duets with Tony Mattola, and later George Barnes. Most of his well known recordings are duets or solo pieces. Here are two examples with a band, and no other guitar player.
Edmund Hall All Star Quintet - Seein' Red
Edmund Hall All Star Quintet - Rompin' in '44
(ok, here's one solo piece) Carl Kress - Sutton Mutton