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I personally wouldn't get in more debt to try to get out of debt. $2k isn't that much money and I'd rebudget and knock it out this winter.
Generally speaking, paying a debt won't improve your FICO score if that debt was reporting as bad. You may have to take other action to help your credit.
YMMV based on the OC/CA. Some leap at the chance to accept your PFD offer. Others won't accept it unless hell freezes over. It's safe to say that most won't accept the PFD on the first try. What I would do is search to see others success in here. I would target those first because they are the easiest and work your way back. From personal experience, some take months and even years before they accept a PFD, even when offering 100%.