I think you should try some summer tires like RE-004...
Why??? As you don't drive your car much, those summer tires will not worn out fast.
In addition, those summer tires are more sticky. So, even 5 years later those summer tires are still sticky. (Summer tires have different compounds, so they become hard and cracked more slowly)
However, those summer tires are not very comfortable and also more noisy!!!
PS: Your driving habit is like that of a super car such as Ferrari owner!!!
(very low mileage)
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