Its unlikely a judge is going to accept another state's SOL. You can try it, but don't be surprised if you get shot down, you're not in NH and a PA judge is not going to know NH law, nor will he try. You're being sued in PA, use PA law !
The part about the account being governed by NH law is in regard to their handling of the account, NOT your LEGAL rights in the state where you live.
As for that waiver, I don't know that they can take away your legal rights that way. Its also unlikely that their lawyer is going to be picking apart the agreement the way you are - you owe them money and they want it. Most of these lawyers are local stooges they hire to sue you in your state. They know NOTHING accept what they are given and rarely have ANY valid proof. They expect to win by default w/o you ever showing up in court. If you fight them and show up in court, 99% of the time they are unprepared.
There can be only ONE 'last payment' date and if you don't have any records of exactly when that was, then you're sunk for sure. Pull your credit reports, now ! Its not unusual for them to fabricate a 'last payment' so you must be certain of when it ACTUALLY was.
The affidavits don't mean squat unless they are signed by an actual Providian person who had personal knowledge of your account and its history. *I* could swear that you owe money - and it wouldn't mean any more than the CA 'swearing' that they know they have the account and the $ amount.
A generic agreement w/o your signature doesn't prove its yours nor do their affidavits. What they provided isn't proof, its bullcrap. What have they provided to prove the amount they're suing for ?? Is there a complete accounting ?? No... so I can walk up to you and hand you a piece of paper that says you owe $xxxx.xx and you'll pay me ?? I don't think so, yet that is what they've done !