Funny about the wobble. I mounted my Shinko the opposite way and no wobble so far. May be way different geometry on my build but you might try flipping it round. I like the tire for dirt roads and pavement. Like to spring for a TKC but not till I win the lottery.
Guess I should mention no speed wobble on the pavement, I do get what I call a head shake after I hit moderate size bumps on a dirt 2-track.