Cold start problems

The 4,000-5,000 does sound a little high but if this only happens at first for a second or two then I suspect this is normal. These vehicles have a programmed strategy that on cold temp days, it lifts the RPM to get it warmed up faster. I understand that what you are saying is it is not good to run at a high RPM on a cold engine but this is actually a bit misleading. When the engine is cold and it is starts running the piston is going to be moving up or down in the cylinder no matter what. So whether it is at 1500 RPM or 4000 it is still going in the same cold cylinder so it is not going to do any more damage. They have found that the faster they get the engine to operating temp the less damage is done. So if the RPM's are higher, it is to get the heat up quicker in the engine.

As for it lurching, that is because the RPM's are high and the fluid is cold. I am not sure you are going to correct it unless you allow the engine to get hotter and the RPM come down.

Next time it is doing it, let it come down to around 1,500 and when you are ready to leave, tap the accelerator slightly and see if the RPM drops a little lower, then put it in gear. This should minimize the harsh engagement.