Safe mode opens more things that you need for the task you are trying to perform. You only need to have the processes open that prevent the computer from shutting down and keeping cmd.exe running.

One thing we haven't tried is trying to figure out exactly what process is making the computer freeze.

Start the task manager in safe mode. Keep the processes tab in task manager open. rearrange by cpu use and then try doing something to the file. When the computer freezes one or two the processes should go up by a lot. If it does then you know whaqt must be stopped. Then it's just to hope it isn't an important process.