You did not elaborate as to the condition of the driveshaft/u-joints. Did you replace the u-joints? A badly worn u-joint (especially the front) can cause the type of vibration that you are alluding to.
Do you have a bent drive shaft? Put the rear of the car on jack stands (positioned on the axle housing), have a helper run the car up to speed while you perform a visual check as to what's happening in the drive line. Is the vibration still felt inside the car as when the car was motoring down the road?
Have you popped the transmission into neutral while at speed where the vibration occurs? If not, try it. Does the vibration change? While in neutral, try running the engine back up to the RPM where you encountered the vibration. Any change?
As was previously stated, a vibration such as that caused by the wrong balance weight on the flex plate is more RPM-specific and not whether the car is under load.
It costs you nothing, at this point, to eliminate other possible sources for your vibration before you home in specifically on the flex plate. Give it a try.
Frank