Well, I think the QP servicing cost is indeed the normal one.
As for the servicing time, it depends if it is serviced in HSWA for instance or sent to Geneva. It seems that it is longer for a service in the US due to the big volume of watches coming back for servicing, considering the staff trained for this kind of complication.
The laser process is used for Pt but also for gold. I understand it is used for dings more than normal scratches and hairlines. Otherwise it is polished.
As for the moonphase disk, I don't know what the cost may be. The latest moonphase are made of Sapphire. If it is the same for your 3940, it must be in good shape not to drop pieces in the watch. I imagine that such disk can be fragile in case of a shock the watch might had. That's just a possibility.
Maybe other members will have other info to share
Best, Mark