The frequently overlooked element is warming up the ears and preparing the brain for that aural demand.
In order to add that element, I use 1A and 1B (I think those are the numbers.). We begin learning that material by playing each phrase and then singing it. As soon as possible, I transition to singing first and then playing. It is important to maintain the aural intensity throughout.
As soon as possible, the first sound that the band makes each day is to sing concert F. They quickly learn to hear and feel that note before the horn even gets close to the face.
The kids can sing and play that F with great focus, tone, intonation, etc. As the material descends, the focus, tone, and tuning become more difficult because of the physics of the instruments. I encourage them to hear the low B with the same clarity, focus, tuning, and tone that they played on the F.
Without moving a slide, the kids can tune and focus even the low C and B with great accuracy. The key to their learning that skill is insisting that they hear each note before they play it.
Silence before the singing/playing is critical because it gives them aural and intellectual space to imagine the note they are to play. Then I encourage them to perform the note without purposeful physical adjustments.
The body can perform whatever it can hear. And it can do that with good tuning and with whatever level of great tone is in the imagination.
With that foundation, we gradually move into more technical playing. For technical passages, I encourage them to hear the phrase and then turn their body (fingers, chops, breathing) loose to reproduce the sound in their imagination.
The more we concentrate on muscular movements, the more we bind our muscles to the pace of our brain and prohibit them from functioning freely.
It is important to continue that strategy into sight-reading and the playing of prepared music.