Agree that this is an insane idea. The registration requirements for short-term stays are not as bad as fully importing a car to stay in Europe, but it is not pain-free. The biggest hassle will be the three months total that you will not have use of the car because it is in port/at sea. The amount of planning you'll need to do also does not make this remotely attractive. Many of the big rental agencies (Sixt, for example) have longer-term rental options which are a far better deal on your wallet and brain.
Source: I imported a car from the US to Germany two years ago. I had a top agent helping me and it still took a lot of time and phone calls.