Actually, Saudi Arabia used this exact same technique to clean up a spill that released much more oil that this. You are correct that their are economics to consider, which is why BP won't do it. Specifically, BP would have to use its fleet of super tanks which are currently full of their other supplies of oil and empty them out and use them to collect the oil and ship it to shore. This was suggested to BP, who responded with a threat to sue those who suggested if they made the idea public.

Download the KML file yourself. The government is lowballing numbers to prevent mass panic. The size of the spill in the links you have given do not match up with the actual satellite images. The government originally reported 1,000 barrels a day and then skytruth.org challenged that it must be at least 5,000 barrels and the government acknowledged it immediately. Skytruth then revised their number after the spill grew 3 times in size over night and said the number must be 25,000 a day and the government responded by saying there is no way to given an accurate number. Skytruth last reported the spill was larger then the Exxon spill and we have heard nothing since. During that time at least two government memo's where leaked showing the government is hiding the actual amounts from the public. Again, don't take my word on it. Down load the KML file from the NASA site yourself. The Satellite image will pop up in Google earth and you can see that the spill is larger then the size of Florida yourself. Also note that the picture was take on May 1st and the Satellite photos from the 2nd and 3rd are hidden by cloud cover so it must have grown since then