Since it runs well for about two minutes initially. I suspect the car has a delayed glow plug extinguish. As soon as those plugs drop out the fuel is no longer burning well.
Thats the smoke you see until the engine warms a little. You could try to fine tune the car but it is really not harmful in my opinion. You could verify this senario by just monitoring the point at which the glow plugs loose their voltage and the smoke starts.
I would attempt to treat the lifters but it may turn out you require a new set. We used to use automatic transmission fluid in the oil but times have changed. Sometimes it helped sometimes not. Some report improvements with a total synthetic oil change as mentioned. Sometimes though they are just worn out.
Louder than a 617 is getting up there. . In general it does not sound like you have any serious problems.
Since you seem to be on good terms with the seller. He might know if the injectors were removed at 100k and checked. I think that is their recommended maintenance requirement.