I also took 6 months LSL half pay, and have now tacked on accrued annual leave and will take another 6 weeks LSL on full pay, finishing up in July. I didn't know about losing super if I was paid out in a single termination payment, which is why I applied for the second batch of leave.
Around my neck of the woods, if you apply for annual leave, provided everyone is not on leave all at once, your request pretty well has to be granted. LSL is another matter and needs to be taken at a time with mutual agreement from my employer. A few years ago, I did have LSL refused by the CEO, after it had been approved all the way up the line, and I was already on leave. When 2 IC asked why, she allegedly said "because I can". My boss and admin were very sheepish when it came to telling me. Apparently they drew straws to chose who would get to ring me up and tell me I wasn't being paid. The power of FU money...what I wanted was time off, not money, so I just stayed on LWOP. Mortgage? Meh, of course I've got enough money lying around to pay the mortgage.