Now that my internet connection is back. . .
Clarence Gatemouth Brown and Fenton Robinson are two Blues guitar players who show Jazz influences:
Gatemouth:
https://www.youtube.com/watch?v=so97HBAuK0o&list=OLAK5uy_lMY8ag3dAxoN340kvYyDvtNZ1wZryS_5c&index=2
F. Robinson:
https://www.youtube.com/watch?v=ukZ-tgkL-U0&list=OLAK5uy_lCU5bRUJRDuY_aaNolkk72S6muiwTzVZ8&index=2
Taj Mal's "The Real Thing" is Blues with excellent use of horns:
https://www.youtube.com/watch?v=JPF485guOH0&list=OLAK5uy_kua_bplHWDjg5KVL29G3JWfyCqNJBptDc&index=2
The group "Room Full of Blues" is one you might want to check out.
Of course, R&B/Blues singers such as Bobby "Blue" Bland and Etta James recorded albums with horns and performed tunes with changes that are more complicated than I, IV, V. An example of this would be the arrangement of "Stormy Monday" on "Live at Fillmore East", which was lifted from Bobby "Blue" Bland. And while the Allmans did not often employ horns, the influence of Modal Jazz exemplified by Miles Davis and John Coltrane is very clear in Duane and Dickie's soloing on tunes such as Whipping Post and Elizabeth Reed.
I agree that Grant Green would be worth exploring. You might find his later material somewhat more accessible, such as the suggested "Alive".
One final note: Jazz organ trios tend to be fairly Bluesy. There are many to explore.
I could on but will stop here.