I've learned over the years to start with the KISS principal. Kiss - Keep It Simple Stupid. How many times have I gone looking for trouble and suspected something worse than what I found? Don't ask. It's just the way my mind works and it's been to my detriment many times. I've wasted more time looking for trouble when it's been something as stupid as for example, a $2 fuel filter.
It seems like the bike may be running lean under moderate load? Sounds like a fuel delivery problem. It's been running fine for the last 4-5 months? What could have changed? First thing that comes to mind that would affect lean mixtures at moderate load would be fuel flow. With that in mind, there's the inline fuel filter and then there's the "other" more forgotten fuel filter or maybe better called fuel strainer on the inlet pipe of the fuel valve. It's primary function is to minimize debris from getting stuck in the fuel shut off valve.
So, a little math here - Most internal combustion engines burn about 1/2 pound of fuel per horse power per hour.
At maximum power, the KZ1300 is reported to produce 120 Hp
120Hp x 1/2 pound per hour = 60 pounds of fuel per hour
60 pounds of fuel per hour / 60 minutes = 1 lb of fuel /minute
Gasoline weighs 6 lbs per gallon therefore the fuel flow required to meet the demand of 120 HP would be 1 gallon per minute/ 6= 1/6 gallons per minute
1 US gallon is 128 ounces x 1/6 gallons per minute = 21 ounces per minute
21 ounces per minute / 2 = 10.5 ounces per 30 seconds
Bottom line after all that calculating, if you were to pull off the fuel line feeding the carbs and measure the fuel flowing out of the fuel line, you should be able to measure 10.5 ounces or better in 30 seconds. That would be the engineered design of the fuel system to support the KZ1300 operating at 120 horse power.
That's the math !!
Wouldn't it have been nice if one of the Kawasaki geniuses put that fuel flow rate in the trouble shooting guide as a simple check to verify the fuel flow coming from the tank???? It took me 4 minutes to work it out but I doubt anyone operating / maintaining one of these bikes would even know where to begin or what to expect / measure if they even did a fuel flow check.