Couldn't have said it better. There's no magic piece either, its really just what your lips and the rest of your body get used to.
IMO, screaming is 25% musical 75% physical. Lots of air, strong diaphragm, fast air, proper embouchure. Back in my hay day (before corps might I add) I go toe to toe with Maynard on his "La Fiesta" F#. I attribute that to HS track workouts and playing just about every day. My lung cap was off the charts.
granted, i'm not a music major and i'm not a stellar tpt player, but I did make the lean line solely on my volume and range. Those were the good old days