My advice for entering any sort of screenplay competition is send your script in early. The earlier, the better.
Why is this important?
Generally, screenplay competition readers are designated scripts as they roll in. If you get your script in early, you will likely be read in a smaller batch and that reader will have more time and attention to give your script.
As for myself, I will be more likely to pay special attention to one script in a batch of 10, rather than one script in a batch of 100. If I only have ten screenplays on the docket, I’m more forgiving and will likely be willing to spend more time with your script.
That said, this might not matter a ton – but even if it matters a little, why not give yourself that advantage?
At the very beginning of a competition cycle, the scripts are sent out as they come in, and readers will generally have fewer scripts on their plate. The closer to deadline, and also post-deadline, those scripts need to get read as quickly as possible, and they will get distributed in large batches.
Just something to keep in mind when sending out your scripts to competitions.