Have you had a look inside the induction pipes? If they have a lot of oil in them, that points towards turbo failure. However, almost all turbo cars will have some oil in the induction pipes, but only a little. Generally smoke on a cold startup is caused by valve stem seals. Often when a turbo fails it will blow smoke constantly. This is not always the case, as if the seals in the turbo are leaking, oil could seep into either the compressor or turbine housings.
It may be worth letting the car sit overnight, then the following morning remove an induction hose before starting it up. That way the engine will not suck in air from the turbo, if it doesn't smoke when you do that, the turbo is the cause. If it does still smoke, it's probably valve stem seals, but it could be oil leaking from the turbo's bearing housing into the turbine (exhaust) side.
Was the turbo inspected when the engine was swapped? I had to change the turbo on a Chrysler a while ago after it failed, the induction hoses were covered in wet oil, but this car smoked constantly when running.