Nice.
For the play I noticed there was a washer that is on the shaft. This is shown in the video. I would make sure it is installed.
Not sure how this particular shift pawl works. Some are stamped out and have rough edges which can be smoothed with a file or a knife sharpening stone. This makes the operation smoother to make it less sticky....
Sorry I don't have more specific detail. The last time I had to change a shift shaft was on my 1974 kawasaki kx125. And that was in 1974!
Jeff