While I really do actually get the concept, honestly I can't say I feel it. Probably the main thing I struggle with in regards to this issue is at what point does one feel closer to, or turn to, Mary, or the patron saint, before God, perhaps seeing her as more compassionate or on 'our side'.
I think you really need to separate those into two issues not one. As pointed out earlier in the thread, believing that any human being, even the Theotokos, is 'more compassionate' than our All-Compassionate Lord is dangerously close to, if not actually heresy. As wonderful as the Theotokos is, she is still a created being. She can no more be 'more compassionate' than the infinite Godhead than she can be 'more all-powerful' or 'more omniscient'.
On the other hand, I often 'feel closer' to my wife, my father, my best friend than I do to God. That doesn't mean they are closer, but limited to my material senses and sinful mind as I am, I certainly feel that way. And while God--being omniscient, being my Creator, having become incarnate--may relate just fine to me, at this point in my progress, I find other human beings more relatable than the transcendent God. If I was a saint, then God would be all I need. But not having reached that point, I still need (or at least desire) the comfort of other human beings as well. And God, in His infinite mercy, gives me that--He has blessed me with a wife, with parents, with friends. He has blessed me with a parish community. And even beyond that, even if calamity tore all those from me, He has blessed me with a patron saint, with other saints that I can respect, relate to, and take as role models, with His own Mother.
One doesn't turn to Mary 'before God' or 'instead of God' any more than one turns to one's family or priest or fellow parishoners 'before' or 'instead of' God. One turns to all of the them *in addition* to God because our fellow Christians, still living, reposed, or glorified, are a community which our Lord has blessed us with.