First off, screaming IS easy. Once you know the technique to rasp your voice without it dying on you, it's just like singing.
Your issue is not the volatility of live music. Your issue is lack of practice. If you can't hit your screams, clean singing, and rasped singing all on a pitch that's musically relevant to the song without "sing then adjust," you need to practice and you need to take lessons with someone experienced in harsh vocals.
And yes, screams have a pitch. It's hard to discern to an untrained listener, but it's there, and you can control it VERY easily if you're screaming properly. The range is usually slightly less than that of your clean singing voice, minus whistle-register witch cackles and the subharmonics you get from pig squeal resonance, but you've got a wide variety of notes to choose from even without using those extended range techniques.
The best medicine for maintaining pitch during transitions between screaming and singing are as follows:
1) Good monitors. Nothing but vox and maybe keys in them, if you can get away with it. Getting some good earplugs works, too, because then you hear a lot less of everything else and a whole lot of you, but you have to practice with them in to adjust to the occlusion effect.
2) Grit glissandos. Pick a note in your comfy range, probably upper chest voice, sing it clean with a raised open palate (ie: big opera voice). Lower the palate until you're in your typical singing voice. Constrict the folds to get the vocal fry going, but maintain that pitch. Further constrict and apply pressure until you're in full-on scream, but keep that pitch going. Take a breath, then transition back down to clean open palate. Repeat backwards (ie: start with scream, transition to clean open palate, back to scream.)
Pair some grit glissandos with diaphragm and open breath excercises and a couple of scale stretches and you've got a phenomenal warm-up for any vocalist that's into harsh stuff. I'd start with diaphragm and breath, then do scales, then the grit glisses, just to notch the intensity up instead of starting with the hard stuff.
Further, someone else in the thread mentioned hearing your pitches before you sing them. If you're not doing this already, take that money you would be spending on a pitch corrector and give it to a vocal instructor, because you need to go back to basics.