The only recommendation for 3K oil changes comes from people who are asking you to pay for it.
I agree that an analysis is the best course of action for you. Your extremely low annual mileage and frequent cold starts will cause a shorter useful oil life (in k's or miles) which makes you a bit of an exception. Only analysis will be able to tell you the appropriate interval.
Other factors to consider are, if the vehicle sits in a garage, carport or in the weather. Does it get an occasional long distance drive to boil out water and gasoline from the oil?
My guess, and that's all it is, is to just change it annually.
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