I had a similar problem on a previous bike (not a Fazer).
After removing the caliper on the offending side, I found it to be the anti rattle spring causing the issue.
It's a thin, shallow v-shaped piece of metal which sits at the base of the caliper and the pads, in turn, sit on top of it.
As it is so thin, it's easy for it to be bent out of shape if removed/replaced shall we say, not gently enough.
If it has become deformed or if any of the lugs are raised, it could prevent your pads returning to their "rested" position in the caliper. This may only be millimetres if that, but that's enough for the pad to remain in contact with the disc and cause the friction.
You may need to remove the spring from the correctly working caliper in order to compare the shape of the springs. If there is a difference, you can use the correctly shaped spring as guide to coax the deformed one back to spec (ideally replace but it will do, short term)
It is a relatively low skill task but patience and GENTLE extraction is the order of the day. There's no point bending the perfectly good one as well by being ham-fisted
I'd definitely check this as you will save yourself a whole heap of time, expense and possibly worse if you continue to use your brakes in their current state.
Whatever you've read about your brakes operating at high temperature to be efficient in the wet is well.....BS
They're not working correctly and my possible solution will cost you nothing, except an hour of your time.
I hope this helps you or someone in a similar position.
p.sRe: Comparing. I've made the massive assumption that 600's have twin front discs. If they haven't, compare with your rear caliper spring instead (they DO at least have a disc at the rear, right? )