Interning is a great way of getting to that point. Working as a consultant is just as great. The idea here is to get into a position where you can show your skills to the people who can ultimately request hiring you - then the whole dreaded HR process is just a formality. Get to know people and make a name for yourself, be the "go-to" guy whom people come to ask. Know a lot of stuff and do good work, then you will be surprised how often you can bypass all the ridiculous HR shenanigans and the rules will be bent for you, backwards if need be. Yes it is hard work but it is productive work instead time spent on polishing your CV to the latest fads, bells and whistles.
And this does NOT mean you have to be extremely out-going or need to have unreal social-skills; you just need to have a "value", you need to be good at stuff.
Call it borderline-nepotism if you want but I am sorry, this is not what they tell you about being hired and it is very real and far more important than all those bells and whistles and "tricks" for applying... and it is all about doing a good job, having a great image and having a high value so they WANT you. Win-win for both sides ultimately.