The choke being out and power comes back is a classic symptom of a dirty high speed carburetor circuit. The only remedy is to take the carb off, open it up and give it a proper cleaning. Honda sells a Marine CARBURETION manual ob Amazon that now makes it possible for a novice to perform the service. Without the manual and the specific information and insight it provides, the chances of success are low.
For a little more than the cost of the manual and some of the rebuild items, you could purchase a new carb.
Then there is the option of having a shop do it for you. But, if they don't have the manual and read it, their chances of getting it "right" are really no better than yours. Not to mention having it done is usually MUCH more expensive.