There are lots of factors that cause the hands off the bar 40 mile per hour bar shake. Worn tires can cause the problem to manifest it self. But there are contributing causes too. Watch out for; out of balance suspension, where both ends of the bike are not reacting to road inputs. The best way to check this out is; to have someone your size and weight ,straddle you bike , raise up on their toes and drop onto the seat while lightly holding the handle bars. The bike should drop evenly at both ends. Have them repeat the drop so you can see how the suspension is reacting to the input. If you are riding with a passenger the drop needs to be done with the passenger on the bike and any additional weight such as 20 lb purses and assorted packing in the bags. Most people when they play with their suspension get the front end too stiff to reduce the natural dive effect of braking.
Since the fjr has very little rear end adjustment, I suggest you set up the rear setting first, then use the multitude of adjustment available on the front end, to match the front to the back. Dunlop tire company made a very important movie years ago called " Wobble and Weave" In the movie they used several bikes equipped with variously worn tires and suspension setting and filmed some of the bravest test riders I have ever seen who removed their hands from the bars of the evil handling creations they were given to ride and were filmed doing it. One of the things they found out was if the bike starts to wobble and weave you can lean forward and in most cases the wobble will go away. Irregardless of this remember; a properly set up bike will not normally wobble or weave especially an fjr. If your bike does there is a fixable problem. Good luck and keep the rubber side down and your smiles up.