I think I might have found a way forward, regarding the harmonic slurs. I managed to fit a cornett mouthpiece to a bugle. It´s a dirt cheap plastic bugle, with not the best of sounds, but at least it lets me practice harmonic slurs from concert Bb to G, which is far less daunting than the full octave from low B to mid-staff B, which is the closest and lowest that the cornett can offer. Maybe if I can make that work, perhaps later I can move on to full octave slurs on my instrument?
I still think it it is worth some effort to try to follow the MTM concept, even though I have such a different instrument. Even after doing a very moderate amount of the most basic exercises, I find I get a more full and resonating sound from the cornett, and with less effort, which is what is all very much about.