Interesting. I saw your comment while looking for a solution to the same problem, including both the Adafruit GPS and an Xbee. To handle it, I'm thinking of perhaps using some kind of logic gate to route traffic from Serial1 to either the Xbee or the GPS. I'm using the GPS coordinates on the Edison, but you may have to load them into the Edison and then regurgitate them to your remote computer.
That's right. The SoftwareSerial library is not supported in Edison and there isn't an equivalent for it.
As Reach41 suggested, you could use external hardware to route the traffic from Serial1 to the devices you have. I recommend you to check the following IC: http://www.ti.com/lit/ds/symlink/sn74lv4052a.pdf, it's a 4-channel analog multiplexer. You could use it to route the Serial1 port to your devices. You could even add two more and have a total of 4 serial devices managed by the Serial1 port.
To update anyone else that may come across this thread, with some help from Reach41, I ended up using the following breakout:
and this blog for understanding how to hook it up:
Since my project only requires the XBee to send data, I only used one of these for pin 1 (TX) on the Edison board so that it could communicate with both the GPS and XBee. Note that each multiplexer requires at minimum 4 digital pins to control what channel your desired pin is connected to, so plan accordingly.