If you really [think that you] want to work somewhere, and this is what I've done in the past, you can just look up their recruiters on linkedin or something and cold call them - most recruiters or HR departments are overjoyed at this kind of personal attention, and can even get you some perks and recognition along the way. Plus you just send a nice email (your cover letter essentially, but not as forced) and attach a resume formatted as you please.

Might not be anywhere near 100% overall but when it works it makes for a really lovely experience.