Very interesting and informative post!
A question: would it make sense to run the k-means after the dimensionality reduction of t-sne? i.e. is t-sne useful only for the visualisation of the high dimensional data?
From what you say it seems that the results of the t-sne are similar to the k-means ones in the original space, so if someone is interesting in the clustering results only, k-means is enough (although a visualisation of the clustering is nice to have as well)