Hi Francis,
I did quite a bit of study of the Balanced Embouchure many years ago when it first came out and found it to have a lot of benefit.
It terms of describing how the lips work when playing it is quite different from Wind-works as BE describes more of rolling in and out to achieve the shape change. More of a focus of top and bottom lip coming together and it advocates for playing with a very small aperture.

The main thing that is striking similar though between the two methods is the way it is implemented. Greg talks about living in one trumpet “building” as you build another with more efficient habits and it takes time before you swap over and this is exactly the same as the BE method. It is also probably the biggest frustration of both authors (Greg and Jeff) that this concept is often misunderstood. In BE there is a roll in exercise that allows for easy high notes, but it only designed to gives the lips that experience and lock away in the subconscious the general movement, however a lot of players get seduced by this and think this is the path to follow for all playing and for the vast majority, it is not.

Just like Greg’s method allows for a phat free resonate sound down low with a large aperture and players get stuck thinking Greg plays all over the horn like that. Perception is not reality.

The rollout exercises can be great for getting the feel of corners moving inwards. That feels helpful for what we are doing in Windworks.
In the end, I haven’t practiced BE for many years now but I do think it is compatible with Windworks IF (and this is the key) you are absolutely clear on the psychology of playing and how doing these extreme exercises in BE is simply to give the lips a chance to experience the full range of motion. In BE there is literally an exercise called “the lip clamp”, which I know is making Greg breakout into a cold sweat just thinking about it, but approached as just another ingredient tossed into the subconscious recipe of trumpet playing it should work.

Worth checking out, the book is cheap and well written and the forum at trumpetherald has the author in there answering questions. As Jim Rohn says: “Be a student, not a follower”

However having said all that, remember the old proverb: if you chase two rabbits, you will not catch either one.

Or I think this is paraphrased from the great Bill Adam, “if you have a foot in one boat and a foot in another boat, you will end up with your arse in the water.”

I hope this is helpful.
– Alistair