The problem I find is that when I add the <SoftwareSerial.h> library, the program stops working.
What pins are you using for Software Serial on the Leonardo?
Not all pins on the Leonardo and support change interrupts, so only the following can be used for RX: 8, 9, 10, 11, 14 (MISO), 15 (SCK), 16 (MOSI).
Does the program stop working if you are not actually sending or receiving but if you just include the library and call .begin()?
Your pwm output is indeed using Timer1, but not any timer interrupts. Software serial disables interrupts on sending.
You may want to take a look at AltSoftSerial which uses pins 5 for TX and 13 for RX.