Took my 8 month old kitten from the east coast to the west coast a few years ago. He’s a high anxiety cat as well.
I leashed trained him so he had a harness, which is beneficial because you’ll have to take them out of the carrier through security. I didn’t use any sleepy/calming things, he didn’t do well with the tests before travel.
I used a soft carrier that could open in the top. He “had” to be under the seat during travel. But after takeoff I just put the carrier on my lap and had my hand in there so he had a familiar scent and touch.
My little guy did very well. His only accident was as soon as I got to the airport so I cleaned him up in the restroom. Use puppy pads. Bring pet friendly wipes just in case. Other than that, it was a lot easier than expected.
My cats had to travel via airplane since I was going to be doing a lot of travel with work. They flew from the east coast to the west coast. My anxiety cat was just as he was before, kept quiet but no accidents this time!
My other one is like yours, definitely a screamer. But he got all his screaming out of the way on the car ride to the airport. He made a little bit of noise while my parents were checking in but they told me he was very well behaved on the flight.
Now all cats are different, so it’s impossible to tell. But honestly I tell myself that if we can survive screaming babies and kids on a flight, then a cat who lets out a cry every few minutes should be nothing