The characeters read by SoftwareSerial are correct (I have checked them).
I don't see how these things you are telling me to look for on the oscilloscope would matter. Why would the steepness of the edges, or 'sharpness' of the signal matter if the correct information is being interpreted by the SoftwareSerial connection? Also, in terms of timing, in the case you are talking about wouldn't some of the information still be being received by the hardware serial, just not the correct information?
Thanks for the help so far by the way. Also, do you have the documentation you read for the differences in hardware and software serial?