As I understand it (certainly in the UK), they do the most straightforward tests first, before moving on to the more complex ones. So blood and urine came first, then ECG, heart stress test before the CT dye test scan and the meetings with the nephrologist and surgeon. They said right at the start that there would be a final cross match (which was done 2 days before the transplant, the day before we were admitted for surgery) just to check there'd been no change since the first crossmatch tests were done.
I guess they could use that as an opportunity for the donor to back out at the last minute should they want to but as I understand it, antibodies etc can change as can whether the donor or recipient is CMV +ve or -ve so there is a possibility you could not be compatible at the last minute.
Good luck, anyway!