You are coming from a bike that turns better than the FJR. Rake and trail specifications do not lie. Add the fact that your FJR weighs in at a ton more, and I would suggest you give it a bit more mileage before you start throwing money at it. Concentrate on riding the curves with the "outside, inside, outside" method. Try to find your slowest speed before you find the apex, hold the throttle neutral at the apex, and apply the fuel just past the apex. This will settle the chassis through the turn and offer you better control. I know that you know this - but with your ZRX, there was a larger margin of forgiveness in this.
Edit - it just occurred to me that the ZRX might be carbeurated. This is significant. Your muscle memory may have you applying the throttle a smidge too soon because on the bike with carbs, it takes a split second for them to react to your input. With fuel injection, the reaction is instantaneous. Coming from a carbed bike to the FJR myself, I do remember this transitions, expecially in the twisties.
Check your pre-load (start with 3/4" sag difference between unloaded on the center stand and with you on the pegs off the center stand - you need a helper). Set the front tire at 40 psi. Rear at 42. I'm assuming that the bike still has the stock POS Bridgestones on it. And now they are 4 years old and if the bike sat outside, with the temperature swings, they are starting to get a bit hard. Check the sidewalls very closely for some microscopic cracks. Look at the profile of the tire from the top for even a hint of scalloping. If either side is even the slightest bit squared off, then I guarantee you that is the problem.
Adjust tire pressure and front pre-load.
Ride it more under a variety of conditions.
Play with the dampening during the day under (as close as you can figure) similar conditions.
After that, if you feel you must try something, I'd try a new set of tires.
