Create a station from one favorite artists. I then add 250 other favorite artists to that station.
Put that station in "Deep Cuts", "Discover or "Artist Only" mode depending on your desire for the day.
Pandora will shuffle among those seed artists and their respective genres ( I range from Pitbull to Bach).
This was a workaround to the fact that shuffle stations ignores each station's mode.
As it happens it is much easier to change from "Deep Cuts" to "Discover" since you only have to change that in one place and not 250 places.
Beware of one issue. you must not thumb up or thumb down any songs. If you do that will bias the song statistics so badly that you will completely lose some genres or have the playlist dominated by only a few. I made the mistake of doing many thumbs. When I noticed the problem, I removed all the thumbs and it was back to a nice random behavior.