The thing with long tones, I find, is to play them long enough to establish "settled openness". It sounds more academic than it actually is - the tone should rest at ease, with no tension, wavering, harshness etc. The goal is more than just to establish a steady pitch, because we're using this as a tone development exercise.
The pitch bend is an exercise to work tension out of the sound by relaxing the embouchure. It's particularly helpful for those who are biting their lower teeth into their lip, which I'm pretty sure you're NOT doing based on the quality of your sound. Nonetheless, it'll still help open your sound up though, and create room for expression. Start working on this with just your mouthpiece alone, off the horn - explore what kind of range you have with it - from as tight as you can flex your lip to as loose as you can still seal air, you should be able to play about an octave, give or take. If you have trouble changing the pitch as you blow into your mpce, try physically opening your jaw as you blow (like biting an apple, but keeping lips sealed). You'll notice the pitch go down, and the farther it goes down, the more air you will have to move to keep the support the tone and keep it steady.
Lower mouthpiece pitch loosely translates into better tone when you put it back on the horn, so the pitch bend with long tones naturally will help you establish where your best core tone is on your horn.
Hopefully this makes sense and will be useful. I'm happy to clarify if need be, just let me know.
And thanks for the feedback on my playing - That A Train track was an encore number after 2 long sets with solos in almost every tune. My face was fried (as was the lead trumpet), which forced me to use lots of space in the solo, and I was quite pleased with the result, which is unusual for me when I listen back to myself. I'm a slow learner, but that was a good lesson about space, and I grew from hearing that recording.
I hope this helps. I'm sure we'll be talking again.