Got a head scratcher I'm hoping someone has solved in the past. My daughter's '88 300TE is losing oil at the rate of approx 1 qt/100-200 miles. There is no apparent leak I can see either on top of or below the engine (I have put it up on a lift) and there is no evidence on the driveway (oil spots). Neither is there any evidence of oil in the coolant. I see no smoke (blue or otherwise) from the exhaust either idling or under power. The loss seems to come when the car is driven at highway speeds. The head looks as if it was replaced recently (I acquired the car last fall). What am I missing? Is there someplace the oil can be ejected at speed that would leave little or no trace under the car? Thanks in advance...

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1999 E320 (gave to daughter) 250K
1994 F150 (may be the end of its road) 240K
1989 560 SL (Reassembly after paint job) 160K
1986 560 SL (deceased., gave it's life protecting my wife)
1988 300 TE (departed)
1994 945T (still running strong with an upgraded cam) 349K
1986 242Ti (deceased)
1968 GT500KR (under restoration)