I'm at a point in the LMS 3.2 install where it looks like its hung on the "Checking locked files...." step. How long should I expect this process to take? It's been going for an hour and I haven't seen anything going on.
Hard to say without seeing exactly what's going on in the installer. However, if you haven't already done the other things I suggested, I recommend you do them. the result will be a much better upgrade.