Daioyu Dilemma and the Senkaku Solution

Most of you are not aware of it, but I majored in Political Science at university (along with a minor in chess and ... um... herbal therapy). My interest in international politics remains keen, and while I usually try to yuck it up here in these posts, sometimes I like to apply my expertise and long experience to the problems of the day, coming to a thoughtful solution.
One does like to be helpful.
As you must know by now, the Chinese and the Japanese have been exchanging unpleasantries over a group of tiny islands north of Taiwan. The Chinese refer to these islands as the Daioyu, while the Japanese call them the Senkaku Islands.
The Chinese lay claim to them because they appear on maps from ancient times.
The Japanese, for their part, insist on their rights to the islands partly because the Chinese signed them away to the Japanese. Japanese have lived on the islands in modern times; there is no evidence that Chinese ever lived there.
Basically, each country has a claim to them, and now that it seems there might be large natural gas or oil reserves under them, both countries would like to strengthen their rights to mine them.
The nastiness took a turn for the worst this past week with Japan claiming that Chinese warships "painted" Japanese warships with their fire-control radar, clearly an aggressive act. The Chinese deny it, naturally, but the unpleasantness has now taken on a darker hue.
The Daioyu/Senkaku Islands, what are we talking about here? First, they are made up of several little islands and rocky outcrops, none of which amounts to very much. The total land area is 7 km² (2.7 mi²).
"How big is that," you ask?
Thank you for asking, because I went to a lot of trouble to come up with some comparisons that would make sense to a variety of people. Their total land area is roughly double the area of Central Park in New York City, for example.
Never been to New York? They are a little over three times as big as Hyde Park in London or a third the size of Richmond Park in that same city. Their land area is a little larger than Lane Cove Park in the Sydney area, one third the size of tiny Iwo Jima, the island fought over during World War II. They are as big as 1307 American football fields (including the end zones) or 980 average soccer pitches. A chunk of Greenland ice of the same size just broke off and fell into the sea.
Anyway, you get the picture. We are not talking about a huge land mass here.
So what can be done about this problem? How can the "It's mine!" "No, it's mine!!" back and forth between Japan and China be resolved?
No, giving them to North Korea is not an option.
In the interest of world peace and win-win solutions to world problems, I have racked my brains to come up with a reasonable solution. The issue that puts a wrench into any diplomatic resolution seems to be the existence of the islands themselves.
"Duh!" You say? "Of course the islands are the problem! Moron!"
Yes, exactly, and I really don't like your attitude.
If you think about it, two important countries are at the edge of conflict over tiny scraps of land out in the middle of the ocean, islands. According to international law, an island is defined as any land that remains above water at high tide, lands that are partially covered at high tide are called "shoals" or "rocks".
The solution to this island problem is obvious. The islands need to be removed.
"HAHAHA!! Moron! You can't remove the islands!" I hear you laughing all the way over here in Japan, and I am really not liking you or your attitude.
Remember what we are talking about here. Only one island stands very high above sea level, Uotsuri-jima with a tall peak on it that reaches 383 meters (1256 ft.). In terms of earth volume they are not that great. Japan, for example, has moved enough earth to build two artificial islands in Kobe harbor, Port Island, built from 1966 to 1981 with an area of 5.23 km² (2 mi²), and Rokko Island, built between 1973 and 1992 with an area of 5.8 km² (2.24 mi²). The total amount of land area is significantly larger than that of the Senkaku Islands. In the United States, the huge Hull-Rust-Mahoning Open Pit Iron Mine in Minnesota covers an area of 13.6 km² (5.25 mi²) almost double the area of the Senkaku Islands, and with a depth in places of almost 200 meters (600 ft.), the amount of earth removed dwarfs the amount that would need to be scoured from the islands.
Removing the islands would be a big project; the removed earth would have to be dispersed locally. The waters are not very deep at about 100 to 150 meters, but there is plenty of room to spread the rock and other island debris so that it does not come above sea level at low tide.
Once removed, the area would be open sea, away from territorial claims by either Japan or China. As part of the island removal plan, an agreement could be reached to jointly develop the resources that might lie below. The former islands, then well below low tide levels, could be used as close-to-the-surface platform bases for oil rig placements. The resource exploration costs could be split 50/50 and any resources developed could be split similarly.
A contentious issue can be resolved in a win-win way for both sides, contributing to area peace and stability.
A Nobel Peace Prize nomination might be in the offing!
And now for the Palestine-Israeli problem... I guess bulldozing them into the sea might be a bit much technologically. You think?