Something to think about...is the wiggle while you're running at a steady speed, or while you're in an accel/decel mode?
Try this test...in a safe, no traffic area:
Smoothly accelerate to about 60 mph in 1st or 2nd. Drop the tranny into neutral and while in a straight line, release the handlebar and coast. Does the bike go into a noticeable wobble/headshake around 50mph?
Don't try this if you aren't comfortable with 1) getting into neutral at 60mph, and 2) coasting down past 50 with your hands off the grips.
When/IF you start to get a headshake, don't panic. You won't go into a terminal tankslapper, but it CAN be disconcerting. Just put your hands lightly back on the bars. The wobble will stop.
I'm willing to bet you start to get a headshake right at 50mph. I've experienced it now on 2 FJRs with worn/cupped front tires. In fact, I'd be REAL surprised if it doesn't, following your "wiggle" description.
This "wiggle" is beginning to be referenced fairly frequently now that the forum is maturing. I'm thinking this is a fairly common problem on FJRs with front tires approaching the 3/4s of their useable life. The first FJR I drove, an 03 with 27K miles, had a badly cupped Avon on the front and wobbled terribly around 50mph. I told the dealer and they took it off the showroom floor until they could get the tire replaced.
My personal FJR is an '04 and the front tire, a Metzeler (gasp!) is approaching the 10k mile mark on the tire (5k in the last 2 months) and it's starting to cup and wobble. I'm going Avons for my next set to see how they do, but it just seems to be a fairly typical problem (cupping) with modern, heavier, more powerful bikes.
Oh, TWN...
So...this male penguin goes out for a Sunday ride and his bike breaks down. Luckily for him there is a garage nearby and he coasts on in. The mechanic says "I'll take a look at it but it's gonna be awhile." The penguin says, "That's okay, I see an ice cream stand just down the road and I think I'll go get myself an ice cream cone." So he waddles over to the stand and gets himself a double-scoop vanilla ice cream cone. It's a little tricky holding on to it with his flippers, and he gets ice cream on his beak and his face. By the time he's finished the cone, he's back at the garage. The mechanic looks up from under the fairing and says, "Looks like you blew a seal." The penguin indignantly replies, "It's ice cream, buddy. I ain't that kinda guy."