You are close. It can depend on if you are talking about the South Sound, North Sound or Hood Canal. Larger cutthroat spawning in the big North Sound Rivers are not available now and won't be until they follow the salmon fry out into the saltwater around April (some smaller cutts are always around though). In the South Sound and Hood Canal the cutthroat spawn in very small creeks and streams and are never far from the saltwater. Therefore, cutthroat are are generally available year round in the South Sound and Hood Canal, but not so much in the North Sound. My summary for the best 4 months would be:
South Sound/Hood Canal: March, April, August, September, October, November
North Sound: April, August, September, October
Like other folks have mentioned, you can catch them every month of the year (especially in the South Sound/Hood Canal). Some people get cranky when guys are catching them during the post-spawning period (spring), because some of the fish are in a weakened condition. If I could only fish for them one day out of the year it would be a crisp clear day in early October with falling leaves and crystal clear saltwater.