Black smoke is not an indication of oil being burned. Black smoke is unburned diesel fuel. Blue smoke or white smoke is oil burning.
Check your blowby. With the engine warm and idling, removing the oil fill cap and see how much pressure is being expelled. Take a video of it, post it on YouTube and put the link here where people can see it.
Consumption under the conditions you describe is often oil getting pushed from the crankcase to the intake manifold as a result of excessive blowby. If the engine that was put in your car sat for a long time, the problem may be resolvable without a rebuild.

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1977 300d 70k--sold 08
1985 300TD 185k+
1984 307d 126k--sold 8/03
1985 409d 65k--sold 06
1984 300SD 315k--daughter's car
1979 300SD 122k--sold 2/11
1999 Fuso FG Expedition Camper
1993 GMC Sierra 6.5 TD 4x4
1982 Bluebird Wanderlodge CAT 3208--Sold 2/13