I have a 2006 FLHTCUSE and it chases every rain groove tar crack and bump in the road especially when it had stock Dunlops. I've run metzlers as the last three tires and now have Avons. Both make it handle these things a lot better but I still get some rear steer in longer fast sweepers if they are at all rough or uneven. I'm seriously looking into the true track.
On the bright side, I also have an 08 FLHR and even with the stock Dunlops I get very little input from rain grooves tar cracks and those same sweeping turns. It handles soooo much better than the FL that is part of the reason I've decided to look into true track to see if I can get it up to par.
I'm not sure the motor mount relocation was the fix for the 08 but it sure didn't hurt. I believe there was a change in 08 to the siwng arm axle bushings that might be the difference. But There is a significant improvement in handling of my previuos 05 RK and my current FLHT when compared to the 08 RK.

The 08 is much better in the twisty's.