I have been thinking a lot about the aperture over the last year or so. It has become much more important to me than the embouchure, because it is more fundamental than the embouchure. It is the vibrating surface that initiates the trumpet tone.
I have one idea about the aperture that can be useful. I got this idea from Kyra Sovronsky at a recent Suzuki brass workshop (and I hope than I am not misrepresenting her idea!). Think of supporting a circular aperture, rather than a flat one. This means a little more support on the left and right sides of our aperture. This helps to control the airstream into being a circular stream. This is perfect for conforming to our circular mouthpieces.

Holding a straw while engaging an embouchure with a light hugging on the left and right side of the straw.
Try holding a pencil or a straw in your lips. Also form your normal embouchure corners, as if you were playing. Notice the pressure on the top and bottom of the pencil. Now try to hug the straw from the sides a little more–perhaps not as much as the top and bottom, but nearly so. I might also add that the lower lips help make this possible more than the upper lips (or so it seems to me).
Now play a long tone on the trumpet, and imagine engaging the same kind of aperture. I believe this is especially helpful for soft, low tones, keeping the lips buzzing when they would otherwise stop.
Of course, if a tone is sounding great with minimal muscle engagement, that’s enough. Don’t try to engage more muscles than you need! Good luck with this concept!
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