Can't get software serial to work
Sender:

SoftwareSerial mySerial(10, 11);  // Rx, Tx


Receiver:

SoftwareSerial mySerial(11, 10);  // Rx, Tx



  I have the 'sending' Arduino's D10 pin connected to the 'receiving' Arduino's D11 pin, and vice versa. 


So you have the sending Arduino's Rx connected to the receiving Arduino's Rx. Therefore it won't work. You need to connect Rx to Tx.



  mySerial.listen();


You don't need that in this simple example.