Suppose McGonagall does not recall being handed 100 Galleons an hour ago. What should she do?

Precommit, give him the Galleon, then reach in her bag to get the 100 Galleons. (She must have been Obliviated; otherwise, she would remember.)

You can actually get around a lot of the problems with time travel by taking advantage of the difference between observation and reality. For instance, if you see one of your friends die, you can go back in time, save him, then plant a fake double so you still have the same observations.