Sounds exactly like what my powerstroke did when it blew a turbo seal... the smoke was a lot more blue than white if I remember correctly. At least this is probably one of the easier things to fix of all that have been mentioned..... just need a good turbo shop and some $$$.

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1985 300D Turbo ~225k
2000 F350 (Powerstroke) 4X4, SWB, CC, SRW, 6spd ~148k
1999 International 4900, DT466e (250hp/660 ft/lbs), Allison MD3060 ~73k