That would be a plan but a side or back step by the nagi will create space so I would say your attack should include faints to cause reaction and allow your movement to close the gap.
The way in on a naginata is going to be the path of focus, wait for the arc to an over commit swing and close.
The real trick is to shadow, once you close you must stay close.
Range is the key to winning for the polearm, take this away and seal the deal.
PS
I use a non traditional naginata technique with a wide center grip, like a long hilted sword but the back hand is far back allowing a quick range extending thrust. I tend to focus on thigh and knee attacks as this throws the whole closing the gap thing off.
