For me, it was, surprisingly, to slow things way down and focus on the quality of each pitch.
My intent was not to increase my ability to slur notes faster, but that’s what happened–among other things, which were all good.
I just ended my practice session this morning and feel like I’ve reached yet another “level” with my ability to slur accurately.
I try to experiment with changing pitch to the next harmonic upward (on the same fingering) using the least amount of movement possible on constant air–by making the air constant (Passively released, not blown), we remove the air from the “equation” and ensure we’re focusing on practicing Shape only.
While doing this, I intentionally do not use a metronome and focus on being relaxed and only changing pitch to the next note up when I’m relaxed and I try to “get away with” using the least amount of movement possible.
This has resulted in my learning how to use more and more efficient Shape.
Tongue arch is part of Shape and helps when slurring fast certain pitches (many of them). Some harmonic slurs are easier than others (Open vs 2-3 or 1-2-3 fingering, etc.). You mention A flat in your post, it does feel like there’s more resistance in some of the notes due to two valves being pressed down (vs Open).
Playing softly, but with good air, has helped me too. When I was younger, I “kicked” with the air to get the higher harmonic and treated harmonic slurs as calisthenic (muscle-building) exercises, rather than treating them more as coordination exercises–which is how they should be treated.
We’re not playing harmonic slurs to build muscle, but to improve our Efficiency of Shape and the balance of Shape and Air.
After spending some time experimenting slowly this way, I would go ahead then and play the harmonic slurs with a metronome but try to use consistent air and play as softly as I could get away with and have a good quality sound.