I agree with your post's conclusion but not the statement above. "The Mikado" wasn't intended to reflect the West's thoughts about Japan at all. It was merely another in a long line of G & S operettas intended to ridicule and satirize British government and culture. The Japanese theme was merely window dressing that gave Gilbert the opportunity to soften his sharp jabs at his own country's politics and institutions by using a foreign setting. He'd done the same thing in several previous librettos like "The Gondoliers."
All this PC nonsense makes me think present-day America greatly needs the services of one of the play's characters to deal with the PC cultural Marxist elite:
"Behold the Lord High Executioner,
A personage of noble rank and title
A dignified and potent officer
Whose functions are particularly vital..."
There is an interesting 1999 movie, Topsy-Turvy, which is supposedly based on the writing and staging of The Mikado, and how it was inspired by the fascination with Japonisme at the time.
More recently, a display in the Boston Museum featuring Japonisme created a big controversy, much like the one we are discussing here, because it supposedly offended people who respect Japanese culture. There were quite a few of us of all political stripes, from Berners to Cruzers, who are deeply into Japanese culture, who all had the same reaction: shut up and show the stuff, it's good history.
There was a Japanese exhibition, in London, at the time that Gilbert wrote THE MIKADO and all things Japanese were THE "rage". No English person really knew much at all about Japan, nor the Japanese at that time, but it was a VERY timely theme to use.
Just as "PATIENCE" was jabs at the "aesthete" movement/Oscar Wilde,"PRINCESS IDA" was poking fun at early "women's lib"/college for women, and parts of "IOLANTHE" had jibs at Wagnerian opera and the English Parliament ( specifically the House of Lords ), and "TRIAL BY JURY", needled the English court system.