Sorry, Lionelsax, all I'm hearing is 'trumpet' on all the videos, except the sax. This is an issue I find a lot of trumpet players seem to have, especially American cornet players because they aren't used to the sweet cornet sound associated with British cornet playing. Give a trumpet player a cornet and he or she will play it like a trumpet, which is fine if it's a long cornet, but is sacrilegious if it isn't. The technique is different, but difficult to explain. It's more restrained and controlled. Expect more back pressure and a less 'open' blow and adapt accordingly.
I'm a bit guilty of this too, now I play the trumpet far more than I play the cornet. If I've been playing the trumpet hard for a session, and try to move immediately onto the cornet, I find I'm treating it too harshly. I try never to play the trumpet and cornet on on the same day.
I've got a long cornet too and it's great for playing trad jazz, but it doesn't sound like my other cornets.