I’m a bit late to this thread, but here’s a 9x9 game me and battleporridge played about a year ago, after a discussion about Thue-Morse on reddit if I remember correctly 
I like the idea of giving double moves now and again, but for me Thue-Morse was too complicated to keep track of in my head, so reading ahead became quite tedious, since I constantly had to check with our pregenerated list of moves. Another way to give double-moves somewhat farily, that is much simpler to keep track of, is to let every third move be a double-move, i. e. repeat the sequence
BWBBWBWW
over and over again. I tried this once, on a 19x19 board, against a player a couple of stones stronger than me. I captured a big group early on after he made a reading mistake, and halfway through the game I was pretty confident I would win. But he adjusted to the new variant amazingly quickly, and managed to catch up and win in the end 
Unfortunately I don’t have a record of the game, since it was over the board and a long time ago, but I’d love to play this variant again if someone is interested 