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I'm having some trouble staying in the high register for so long and keeping a good tone. Any suggestions?

How does a marathon runner get into shape for a race, he doesn't rest, he runs distances close to the distance of the race or even longer so that he does not tire during the shorter race. Play until you stop playing with the sound you want, then take a break, go back and play some more. Eventually you'll develop some endurance up there, its not overnight, but it will happen. Also make sure you play low tones often enough to balance out your playing so that you don't change your embouchure entirely.