THX TEX!! I LOVE YOU TOO!!!
Alright so as far as my inspirations go:
0:00 - 1:11 is Early New Orleans style jazz, the first type of jazz to exist which was played by Creoles and Black people when the Plessy vs. Ferguson act enforced segregation, declaring Creoles Black and forcing them to play with Black musicians only. The two ethnicities' styles of music mixed to create jazz, which was often played in jam sessions at clubs in New Orleans in places like Dixieland (hence this style also being known as Dixieland which I literally just found out by looking at Wikipedia). It is characterized by its use of collective improvisation, where each member of the band is playing their own improvised melody along the chord progression. There are a few songs with exceptions to this rule, such as
Chimes Blues by King Oliver's Creole Jazz Band, where Louis Armstrong played a prewritten cornet solo. That aspect in particular seemingly lends itself to the writing of faux-collective improvisation in a DAW, since every instrument meshes together too well to be true.
Everything past 1:11 is Swing, the famous pop music genre of the Jazz Age and beyond. It took me a couple listens to figure out how to get the instrumentation and drum sound design down, specifically
Take the A Train by Duke Ellington & Billy Strayhorn, In The Mood by Glenn Miller, and
Well Git It by Tommy Dorsey.
Swing sometimes features a call and response between one or more lead instruments and supplementary instruments providing chords, for example a saxophone and muted trumpets respectively. Then at 2:38 the solos: A keyboard (Organ 4) and a couple others halfway through, and then a drum solo. I took inspiration from
Sonny Rollins' song St. Thomas from Saxophone Colossus for those sections. Please listen to it, it's got some of the best solos I've ever heard.