As BoilerUp says, you need cultivate relationships. I would say 99% of the best corporate jobs are aquired through recommendations from within or from peers (manager to manager). This will get you in the door, but won't necessarily get you hired.
The hardest thing a hiring manager has to do is find someone who will fit into the culture of the department. This has nothing to do with flight time, it has to do with your attitude, appearance, and your interpersonal skills. If the culture requires people with blue hair and you have red, guess what, you won't get hired. I suggest you seek out jobs where you think you will fit.
Another thing the hiring manager might consider is if you are local or not (live within 1 hour of work). If you are local and fit most of the mold, this will be in your favor. (Of course, if you are the perfect candidate, it won't matter so don't let it discourage you).
In my company, if you sent a letter to the President or CEO it would not help at all. I would stick to the Director of Operations or the Chief Pilot (who are normally the hiring managers).
So, if investing the time in networking is not an option, you might need to create a spiffy looking resume that might stand out in the pile of the other resumes with 5000hrs jet and 4 type ratings

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Kevin