On a cheque clearing - I had a super rollover cheque that I had to clear days before my POK options expired. I took it to my bank (ANZ) on the morning I got it and asked for a priority clearance. They said it would be in my account late that day - and it was (which is quicker than previous priority clearances I have done).
So hopefully Doughr, you can do the same with your bank - and get the same result!