Arrival at 4:25PM and departure from Haneda at around 8PM, I think should be doable. Transfer time from Narita to Haneda is about 75 minutes by bus and takes 3,000 yen:

http://www.limousinebus.co.jp/en/tim...r_tokyu_h.html

That leaves a little over 2 hours for immigration, bag pickup, customs, traffic allowance and domestic check in.