Why not have a look at the spark plugs? If they are Oil fouled then you have a clue... if they are full of soot/carbon you have a clue.... Yes 1 quart of oil per 500 miles is heavy. are you sure that some of the oil is not leaking out of the engine due to old seals??

If the plugs imply it is oil:
I have used some snake oil called RESTORE on a briggs and stratton engine, that puffed white/blue smoke all day long, in fact it used half a pint every two hours, and the spark plug would foul almost daily.... I got sick of it, and added a half of a can of restore and it polluted less, had more power.. and got me through the season of resurfacing tennis courts.

If the plugs imply it is a fuel condition:
Does it only happen at 5000 RPM? and under a load? have you got a lot of oil/mist comming out of the valve cover when the engine is warm? It could be a overly rich condition, where the exhaust system is loading up with carbon, which does not come out until a High RPM load, thus high volume of exhaust sweeps carbon out... May be it is a lazy oxegen sensor....

May be it is none of the above.

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46 WDX Power Wagon

84 300TDT daily driver