I would think a modern oil like Mobil 1 or another synth could go for 6800 mile without changing, even the break in oil would make it that far without damaging the engine.
Sorry to hear about your problem with the engine. I agree with 8 image GIF guy, I would ask nicely for a buy back / replacement since it's brand new. I check my oil about 1 time a week, the same time I check my clutch fluid for changes in color, crap content and change the clutch fluid if needed.
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