Topic votes also work in categories where users have the ‘see’ permission, but can’t create or reply.
Using a link to create a pre-filled PM to a group mailbox as per this guide:
Would create an initial manual step for said moderators to move entries across into the competition category, but from there they could be voted on with no commenting possible. If there’s any entry criteria for the competition then topics could be vetted at that stage, or just moved in bulk a few times a day.
As the number of topic votes is limited by default will you be allowing votes to be cast before all of the entries are received?