With improved oils and larger crankcases on modern engines (how many quarts does yours take?), combined with your high yearly mileage (3,400 miles a month - wow, that has to be largely freeway miles, right?), I’d follow the 10k recommendation. Modern BMWs are often over 12k, many GMs on their oil monitor systems go 8k.
Does it recommend full synthetic? Given that this is your home, I’d be inclined to use an appropriate full synthetic oil