I did have white smoke on my td4 some while ago. Turned out to be hp pump pushing diesel into the crankcase and the engine breathing it. Mine also ran on without key in so be careful!!
Yes, blowing past seals and into timing cover - feeding high pressure diesel vapour into crankcase ventilation - it ran well ! More smoke than yours but white and at tickover too increasing when revved up.
Today tried another crankshaft position sensor, because unburned fuel could be result of bad timing. Without any success. Same white smoke on higher revs.
Engine starts fine, have nice idle, almost without any vibrations, all good until pressing accelerator.
Stupid question, but it cannot be fuel filter? Just maybe HP pump receives lower pressure and cannot send to injectors good strong amount of fuel, and injectors can't make good pattern?
Video of idle:
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