I play Flugel as my main instrument (Brass Band), and get the right FLUGEL mouthpiece for the instrument. Don't try cornet (too small) or trumpet (too shallow) mouthpiece.
With the right one C and D above the stave are about as high as you should ever go (it's a flugel) and the bottom notes should be easy enough.
I also play trumpet in an orchestra, (and cornet elsewhere too) and use a mouthpiece for the instrument, without worrying what I use on the others.
My flugel would cost $4500+.