It's Jack Jackson, absolutely! All the hot trumpet solos on Jack Hylton sides recorded between September 1927 and the end of 1929 are played by Jack Jackson. He was replaced by the French cornetist Philippe Brun (another Bixian player), who stayed with Hylton from January 1930 until returning to France in 1936.
Jack Jackson seems to vacillate between Bix and Nichols, as so many white trumpet/cornet players of the time did. Rob, you'll remember highlighting Jackson's Bixian solo on Hylton's "Oh! What A Night to Love" when you reviewed "The Influence of Bix Beiderbecke" CD set, and I also well recall your finely tuned ears spotting that Jackson interpolated Bix's second break in "Riverboat Shuffle" into the start of his solo on the Crichton Lyricals' "Somebody Said".
Jack Jackson's solo on "Oh! What A Night to Love" includes a "rip" (flaring up to a higher note), something he presumably learnt from listening to Bix and/or Nichols recordings. But who used this technique first (at least on record) - Nichols or Bix? I think that it's probably Bix. Nichols plays a great rip on Sam Lanin's "Clap Hands Here Comes Charlie", recorded on November 27, 1925, but Bix plays a rip on the Wolverines' "I Need Some Pettin'", recorded nearly a year and a half earlier, on June 20, 1924. I can't find an example of Red playing a rip that pre-dates this, but I'm open to offers!
And what about half-valving? Both Nichols and Bix half-valved. The earliest obvious recorded example of Bix half-valving I can think of is his break on Goldkette's "I'm Looking Over A Four Leaf Clover", but he sounds like he's using the half-valving technique at the start of his solo on the Wolverines "Copenhagen". Again, I can't find earlier examples of Red half-valving.