You might want to investigate air freight. There are a surprising number of charter air carriers in Iceland who operate wide-body aircraft (thus suitable for motorcycle transport - you just put the moto into a ULD and strap it down).
My past experience with air freight - many trans-Atlantic shipments of my Honda ST1100 - has been that if you find a charter carrier who operates widebodies, they almost always have excess cubic capacity on the lower deck. Relatively speaking, a motorcycle weighs nothing (compared to a fully laden ULD, which can be up to 8 tonnes). Thus the air carrier is usually quite happy to sell you a spot for a reasonable price. Often, you can buy a ticket for yourself on the same flight.
The DGR (dangerous goods regulations) for transporting motorcycles as air freight are not cumbersome. The moto is classified as a 'vehicle - flammable liquid powered' and falls under packing instruction 900. Provided that you tie the moto down in the container in such a way that it is not reasonable possible for it to fall over, you only need to show up with less than a quarter of a tank of fuel. There is no need to drain liquids from it, disconnect the battery, or any other actions like that.
However - be darn sure that your moto is scrupulously clean. Take it to a coin-op car wash and give it a good blast, making sure that you get all the dirt off under the fenders and all the bugs off the front of it. I have never encountered any difficulties with importation arising from licensing or insurance, or any difficulties with shipment arising from fuel or saddlebag contents, but I almost always get challenged by some agricultural inspector who is worried that I will be unintentionally importing an exotic squashed insect or a blob of soil (dirt) containing some kind of killer fungus or bacteria.