I was able to get one Mini-PCI modem from a current model ThinkPad. It appears to be manufactured by Ambit (couldn't find web site).
I was able to find something on it here:
Drivers are easily found on IBM's web site. I will try to have pictures and links as soon as I've had a chance to test this.
Please note that I only have one of these cards so I'm not prepared to offer them for wide distribution. I'm only doing this as an excercise to find a potentially better modem for the Web Player. The difficulty is going to be connecting the modem since its connector is very different from what's in the Web Player.