You might consider mentioning your anxiety to the gate agent or flight attendant and asking if you could introduce yourself to the pilot. I know that might sound strange but several years ago I was operating a flight and the gate agent approached me about a passenger with anxiety that wanted to speak with me.
It turned out that the passenger was part of a support group for fearful flyers and this flight was her first. Fortunately I had a bit of free time before departure and was able to show her weather reports and a few things in the cockpit.
It seemed to be reassuring to her to meet the pilots.