Final update: Waited for the rain to stop then swung out to the next best auto parts store, and borrowed a pair of vicegrips and two pairs of pliers. An hour or so of fumbling with the regulator and I was able to get everything fixed.
You do NOT need to remove the window in order to fix/extract the regulator.
You do NOT need to cut any part of the old regulator, as I have seen in some other posts. Just carefully bend the capture tab at the top end of the regulator by the wheel and the white clip should slide right out.
You do NOT need to disassemble any part of the regulator beyond removing the white clip. You should be able to pull on opposite ends of the wire, and the captured springs by the motor will give you enough room to pull the wire tabs into the white clip.