You're correct. SoftwareSerial library is not supported by Edison.
Without more information, like what speed you need, do you need multiple UARTS, Input or Output or both, it is hard to give a full answer. Also note, I am rusty right now doing stuff on Edison, so take with grain of salt.
My guess is that the standard SoftwareSerial library will never be ported over to the Edison, as it is highly dependent on AVR architecture. That being said that is not to say that one could not develop some form of Bit Bang Serial Output and/or Input. . However you run into several different issues.
IO Speed: I am not sure how much this is an issue, You can get reasonably fast IOs on several of the IO pins using memory mapped IO... Again depends on what Baud rate you are after.
Bigger problem is you are running under Linux and probably not a real time kernel. That is when you do something like: write a byte out over a serial pin, you have timing requirements of how long the pin should be held high, how long it should be held low... Problem is your code may be not running when it is time to switch the IO pins state (or read it if you are doing an input). If you are doing low enough baud rates, your code will hopefully be called fast enough such that you will do the IO transition close enough in time to work. However the faster you go baud rate wise, the lower slop factor time you have.
Maybe at some point, you can use the third processor (Atom) for this. I believe it was the last (current) release that added some support for the Atom, but if I remember correctly it was rather limited and when I played with it many months ago, it appeared like IO speeds were slower than using the main processor.
Not sure if my answer helped here, but thought I would give my 2 cents.