This is why I questioned this at the outset. It appears you're not the one who designed this but at least you are smart enough to ask questions. It's good that you are, somebody needs to. Lots of people have misconceptions about what you can and cannot do with VFDs and someone may have misapplied them here. It happens a lot unfortunately.
When you run a motor above base speed, you are running in Constant HP mode, which means, as noted, your motor shaft torque is dropping proportionally to the speed increase.
In a centrifugal fan, the load torque requirement is INCREASING with speed. If you want to move more air, you need MORE power to run the fans.
So in this application, these two issues are at crossed purposes. At 90Hz you have cut the motor torque in half while the HP at the shaft remains the same, and at the same time you have created the situation with the fan that it is now demanding 337.5% of the HP it would at 60Hz (power increases at the cube of the speed change in a centrifugal load, so at 1.5X speed, the fan will required 1.5 x 1.5 x 1.5 horsepower). The only way this will work is if the fans, and the VFDs running them, are over 3X the size you would use at 60Hz. So in other words if you needed 3/4HP at 60Hz, you have better be using a 3HP motor to run it at 96Hz.
If your motor is not over sized, running it with lower output torque by running over speed puts it at risk for running at higher than rated slip, which indeed increases current draw and therefore heat in the motor. While it's true that some types of motors with fan cooling will get more cooling as well, there is always a chance it cannot keep up. If you have a TEFC / TENV motor it may not be able to take it at all.