I suppose I was looking at July train schedules (which was a quick way to estimate when not knowing the actual date), but still, going via Hamamatsucho is close to impossible.
Back to the topic, you probably ended up in the same situation even if you had booked directly to ANA. Like you said, it's a flight itinerary that ANA approves, and Priceline is a mere agent. That's how it works. They give you outrageous connections and outrageous delays these days, wherever you book.
You can try contacting customer service of both ANA and Priceline again and again to get your flight changed free of charge. They won't be risking much by changing flights, unless your departure date is extremely close. On the contrary, they need to expect harsh complaints if you can't make it to that connection.
Meanwhile, according to Taxisite, a ride from Narita to Haneda, with
late-hours fare added, is approximately 29,710 - 29,890 yen using the Expressway, and takes roughly 60 minutes.
http://www.taxisite.com/far/anytoanyret.aspx?night=1&hway=1On the bright side, 7,472 yen per person is not a bad deal, keeping in mind that if you use other transportation means it will cost you half the price anyway and takes you more time and energy. Let's just hope that the scenery from your window and the chat with the driver is worth that price.
Needless to say, when you get to Narita, be sure you head for Haneda anyway one way or another, because that's where everything is convinient, and you don't want to miss any alternative flights (unless they decide to book you a flight leaving from Narita) .
I truly wish you good luck, whether it's for a complaint or time or driver. And take it easy. Like they say, "Better late than never"!