I would suggest- pictures of the damage- along with a well drafted letter, that is short and sweet- describing your damage, date it happened, and the cost of the loss- to the president of Alaska Airlines and the chairman of the board- with your MVPG number, and a list of all the flights that you have taken this year.
The responsiblity begins at "the top of the heap"- and if they do not know the problem- directly from the customers - they do not know how much a problem it is to thier customers. If enough customers, take the time to write, upper management is bound to take notice-
I have made it a pratice to write- directly to heads of companies- with complaints and also will write complementry letters re an empolyee- and send via USPS- and if I really want to get attention- I send it with delivery reciept request- Most of the time, I get an answer- many times positive results - sometimes nothing. You may not get any $$ for the damage- but it will not be "blown off" I am sure. What ever you get- is more than you have now.