If it were me, I would call my bank and ask them to raise the daily transfer limit (if you cannot do it online).
It can be reduced back to $20k a day later or so if you wish.
I'm not sure about it being done incrementally. Why risk it if you want to put in more, call the info line to clarify if you'd prefer to not increase your daily limit.
Info line noted in booklet 1300 648 874
