I’m NOT trying to be toxic or to say who is and isn’t able of soloing the Chess Event, but several years ago, I had a friend complain that it was impossible, that Blizzard had made it so we couldn’t solo, etc, etc.
So I made a video on youtube called “Karazhan Chess Event Solo (March 23, 2018)”. Search that exact title (it’s my name in the channel) if you want to try my strat. It ALWAYS worked for me, and only a couple times I had to do a second attempt… and I done it dozens of times.
It’s horde side, but I guess you can simply do the same on Alliance (maybe bloodlust is something else, I never tried the human king).
The interface addon I used at the time may be slightly confusing, but the only thing I was doing there was hitting the button to exit the piece that the game puts in our action bar (not the leave vehicle button from some addons), running back, waiting the short CD, entering another piece, etc, etc.
Hope this helps!