I think the reason why the symphonium in the video doesn’t sound good, is that the mouthpiece is oval or round, and the diameter is too big.
If I were to make one, I would use the Hohner Student 32 melodica plastic black mouthpiece: this has a round opening at the end, but it begins with a very thin flat opening.
When you want to exhale really hard and you want to produce a loud note, people tend to close their lips together. So the O-form of the lips changes to a more closed form. That way you can exhale with force.
Try to exhale really hard and at the same time keeping your lips in an O-form (oval or round shape), it’s impossible.
I think the Wheatstone Symphonium could work better with a “melodica mouthpiece”.
But because I don’t have a symphonium at home, I can’t test it…