The most obvious way to describe in an effective and truthful way the very serious problem of pilot fatigue to the general public would be to simply join a pilot for an entire block of duties during a busy roster period. Just follow him/her from leaving home to getting back home. The key is the pilot should not be chosen by the airline, it should be the pilots to send copies of their rosters to the journalist and invite him/her to join for ablock of duties which is truly representative of the toughest blocks he/she is used to fly.
My suggestion is: ask all low cost airlines in europe to let you follow a pilot in his/her duties for an entire block of duties next summer, adding that they should let their pilots know about the initiative so you can talk to them see their rosters and choose a block that is really representative of a potential fatigue situation. If the reply will be "no" then ask why and discuss.