[so, going up to the timeline, Grell proceeds to put a little flame doodle on 1:45 am.]

After the fabric was burned, I took it upon myself to check the incinerator to see how quickly it cooled down. It took about forty five minutes to get to the point in which Adam found it, which means our culprit activated it somewhere in the ten minutes before 1:45 am. So, that gives us a tighter window to look at.