That was my first thought too

is there a damper on the bike? though my SRAD hasnt got one and doesnt do that, Ive not heard of that on Fazers before but then I would imagine not many Fazer owners would take both hands off at once.
Tank slappers are usually through hitting bumps/ripples in the road nd increased weight on the front together with the bars moving left to right at a certain frequency-its self perpetuating the slower you go the worse the slap gets just like rolling round off the throttle without damping any movement on the bars with your arms. Riding that bike in that state no hands long enough by the sounds of it will end with your face and chest on the ground if you are unlucky.

Opening the throttle removing weight usually sorts it out, it always has with mine and Ive had2xsevere episodes, being on full throttle with gears to go meant I could ride it out though. Maybe your shocks arent damping the small undulations- you may have stiction on the forks? no bar end weights or steering damper if they had one OE? fork rake at the wrong angle ie too much rake like a chopper which you are makinworse by sitting backwards will have the same effect- the front wheel just want to tuck all the time?
Many possible causes and 1 immediate solution for now, ride with at least 1 hand on the controls untill sorted. Let us know what you find