I'm sure you've tried to explain this to him, but anything you put on the lawn now to control moss will have the same results - the moss will turn brown. And depending on how widespread the problem is, the lawn will look far worse for the near term than if left alone.

Moss in the NW is the result of several problems - soil with low fertility and that is excessively acid, compaction and our climate, which is usually a combination of too much wet and not enough sun. Correcting the development of moss under these conditions is not an immediate fix - it takes time. You could certainly start the process now, but it is too early to overseed and your client may not be willing to wait for the results he is expecting.

The best part of moss in NW lawns is that it is uniformly green and rather lush looking, specially at this time of year. If he wants something that looks decent for right now while the house is on the market, I'd convince him to just leave it be. The tidiness of the garden and the house itself is going to clinch the sale, not that the lawn is or isn't of golf course quality.