Heet, Did you buy this bike new? I didn't see that you every posted what year it is, or whether you bought it new or not. It sounds like it is possible the bike has been wrecked. As everyone else here has said what you have experianced is not normal for a FJR. Even if you bought it new it is possible that either the dealer you bought it from wrecked it before you bought it, or if the dealer got it from another dealer, that dealer wrecked it.
Another question is whether you had the bags and top box empty when you and Wildman test rode it. Everyone forgets it, but Yamaha has always cautioned owner to NOT use the top box and saddlebags at the same time. I know a lot of people do, but Yamaha says not to. It may be interesting to ride the bike without any luggage just to see if it makes any difference.
I find it interesting that the question of what brand of tire was installed to try to fix the problem, but it has never been answered. Why is that Heet? There have been many people who got the same type of wobble from Avon tires. I have experiance the same thing on other bikes when I got a old tire that had been collecting dust in the back room for a few years before I mounted it.
What the dealer was talking about in regard to turning the screws is the mixture screws that adjust the throttle bodies. My dealer did the same thing the first time I took it there. They backed all the screws out so far that you couldn't adjust the idle speed.
If you state has a lemon law, use it to make them buy it back.