With respect.... as jdallen
says, it is very clear that you have absolutely no concept of the scales involved here.
Perhaps you're aware of our Herculean efforts to tame the Mississippi River, which at peak
flow, represents 2% of the flow through the straight. By the way, that project has cost ~7 billion, and the upkeep of the structures is a constant uphill battle.
How exactly do you propose we tame the unfathomable forces behind the transport of 15.8 billion gallons of water per minute? With dredge? Seriously? That's 15 with nine zeroes behind it. You are vastly, vastly underestimating the power of water, the ocean and the harshness of the Arctic here...
We could probably do it - If all of humanity were to get behind the idea, and every nation that could were to pour money and resources into it. Manpower, equipment and money.
And we don't even know if it would work, nor the possible undesirable consequences. There is no way that this will ever happen.
That money and effort would be far better spent on 1) transitioning from fossil fuels or
2) More space exploration; Colonizing mars, etc.
We are well past the point of state change - in fact, it appears the state change happened way back in 1987http://onlinelibrary.wiley.com/doi/10.1111/gcb.13106/abstract
. An ice free arctic is inevitable with CO2 at 400PPM and climbing, just a matter of when the new stable regime is reached. That doesn't mean we should give up the good fight, but this is not the solution.