I don't think that's oil you're burning, I've never seen oil that burns white, sounds more like antifreeze that is some how entering the combustion chambers, if the top half of the engine was replaced 10k miles ago then there might have been a problem when the head was installed that got manifested with the extended 500 mile trip where the engine is turning 2700 to 3000 rpm's for a long period of time, perhaps as long as 4 hours at a time before you stop for a break. Its a lot different than driving 1/2 to work or a few miles to the mall. Maybe the torque sequence was wrong or the head was warped slightly.

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87 300d Turbo 241K with original #14 head (blue)
87 300d Turbo 198K will run great again someday (silver)
84 300sd sold ( buyer drove it to Paraguay )