not entirely sure how to test the map sensor but my good old trusty haynes manual says that you just need to make sure the vacuum hoses and wiring are securely tight but one way i would try is too disconnect the wiring for the sensor, drive it for 5 mins too see if its got worse or stays same as b4, if its same then the sensor is broke. As far the wastegate been faulty or stuck half open i was told that you will get a lot of excess smoke especially first thing because it wont direct the exhaust gases to the turbine but i think the wastegate uses the map sensor to determine the pressure in the inlet manifold those whether to send it to turbo or straight to exhaust.
Lastly i would not rule out the inlet temp sensor (intercooler sensor) because you said it slightly improved after reconnecting the wires, so it maybe covered in crap and giving a miss reading