CC3000 WiFi Shield [SPI] & CN-06 Ublox GPS [Software Serial] Not Playing nicely

Hi folks,
So I've found myself in a bit of a predicament. I have an arduino uno r3:
a variant of the CC3000 Wifi shield sold by adafruit:

and a Ublox neo-6m GPS unit:

My intention was to connect the GPS to the Arduino+CC300 shield combination and transmit/push GPS data to a website every 20 minutes or so. I've managed to get the GPS working by itself; spitting out lat, long, date etc. and I've also managed to get the CC3000 to connect to my wifi network and successfully ping websites etc.

My dilemma arises when I combine the two and try and read data from the GPS and WiFi shield in the Serial Monitor. I'm using the NewSoftSerial that's in the core arduino v1.0 and I've configured the GPS to connect to pins that don't interfere with the SPI connections that the CC3000 uses.

The GPS operates at 9600 baud and the WiFi at 115200 baud. I know from extensive googling that the Uno can receive inputs from different devices at different baud rates however I'm getting no data from the GPS when using the WiFI shield. Is this because it operates at a different baud rate or is it because the SPI and Software serial don't particularly like each other?

I'm not overly fussed if I can't read the GPS data in real time through the serial monitor but is it possible to push the data via the CC3000 to my website?