Ok, at the risk of coming across as a naive newbie, let me say what I think a professional trainer like Barbara Heidenreich or Chet Womach would recommend. I took a quick look through Barbara's site but couldn't find the article and therefore couldn't paste the link here.
There's basically two things you need to do. Neither is quick, but both are relatively easy. You need to extinguish (that's the term she uses) the current behavior (Beau panics and chews cabinet when Fred screams), then redirect Beau to exhibit a new behavior whenever Fred screams. Sounds easy, but there are people out there who make their living training stuff like this (I'm not one of them).
First thing to do is identify a behavior Beau currently does which would be an acceptable replacement for the cabinet chewing behavior. Maybe, for example, Beau is a tail chaser, or maybe he can stand on his back legs. Capture that behavior and put it on a cue. There are a number of sites out there (goodbirdinc.com and birdtricks.com) which will show you how to do this through clicker training. Based on my experience with my dogs and my daughter's Conure, this first step will take about a week--maybe two. When you're done with this first step you might, for instance, be able to clap your hands twice and Beau will chase is tail.
The second step is to transfer the cue from clapping your hands to Fred's scream. You start out by clapping your hands whenever Fred screams, then rewarding Beau when he chases his tail. Do that for a week, then attempt to eliminate the hand clapping and watch to see if Beau still chases his tail. If he does, or if he even attempts it, reward him. The screaming is now his cue to chase his tail. This substitution of behavior is called redirection because it give Beau something to do which is less likely to result in an increased feeling of panic, to say nothing about also limiting damage to your cabinetry.
Now I've probably got something wrong in my description, and hopefully some of the more experienced trainers out there can show you a better way, but I thought this might be a method worth trying before you resort to casting off a valued companion.
By the way, the more I think about it you might not want to use clapping your hands since that will likely reward Fred for screaming, and you might not want to use chasing his tail since that will probably make Beau dizzy if Fred starts up an extended screaming session. You get the idea though.
Good luck!