Best way to fix LinkedIn's recommend system is to stop using LinkedIn.
Scenario: I want to talk to a person with this title at this company. Cool this guy has the title, but I can't get to him. Look up the last person with the title, call and ask for that person and get transferred to the new person. There are 1000s of techniques to use LinkedIn.
LinkedIn > Facebook > Twitter - I pity those who don't see it.
With that, and a network of actual working professionals willing to vouch for me, I'm hoping that when the opportunity for real work arrives, employers might actually take that crucial second glance at me.