Should you not go above max VGS for a Nmos?
Max VGS is given in the Absolute Maximum Ratings section of the datasheet it is given as 16V in the one I have seen for this device. irflz34n datasheet

The number you are looking at is the threshold voltage which is where the transistor is fully on under low current conditions. It is given a minimum and maximum value for any one transistor because of variations in manufacturing changing this value. This is not intended to give the operating range for the transistor.

Using the transistor as a switch it is good to drive the gate higher than the threshold voltage. Somewhere in the data sheet you should have a graph of either RDSon or drain current at various gate voltages. From this you can see that the ability to drive higher currents is better as you drive the gate voltage higher.