People are likely to cheat toward the end for a different obvious reason: namely that their estimate of impending poor success more and more accurate as the end nears, and so the pressure to do something to improve the outcome increases.

(This is in a different setting, when there is some limited time to achieve some predetermined, measurable goal.)

When the pressure sets in is when people start cutting corners, and that can come simply from being closer to a deadline while lagging in progress.