Get a wand and bind a cheap (mana wise) attack spell to it and blast away, as you said can only have six in a deck. Seeking dispel make a good counter. When you have initiative, hit him with your bound attack spell then a Hurl boulder.
Buff up on your equipment and melee him when you start rolling 6-8 dice, Nullify will be the last card he will have time to play. Then try the Attack Spell/Hurl Boulder combo.
Have a familiar cast spells to trigger the Nullify, then hit him with something good.
The point is, if your opponent is playing Nullify heavily, then counter with a plan to make them useless. It won't take long and you will no longer have 6 of them in either of your books....