I'm taking inspiration from @xenoid's answer to Is there any hope for making this site about photography?:
Maybe the weekly contest is a wasted occasion? Instead of adding a picture as an answer to a question that most people don't see, how about posting the picture as a new question with a weekly-contest tag so that everyone can give their opinion? I learned a lot from reading comments about other people's pictures.
In this new method, every entry would be posted as a new question on the main site. Then, the winner would be the one posted that week with the most upvotes over that week. (We'd no longer have the "rolling" aspect. Or, if it turns out there aren't enough good entries, there could be a vote t threshold and if nothing beats that in a given week we could turn to older posts which have accumulated significant upvotes but did not yet win.) A Data Explorer query could be formulated to make it so the mods running the contest don't need to do a lot of manual tallying.
I know we've generally seen this kind of "not a question" critique to be problematic (see for example Can we re-open the door to something a little like photo critique? dating way back to 2012), but perhaps there's room for it within a special tag. We could make it clear in some way that questions in weekly-contest are special and answers are allowed to be feedback rather than proper answers. (Moderators, are there site features we could use for this?) Also as a deviation from normal practice, we could have each question title start with "Weekly Contest: ", in addition to the tag, in order to signal that these posts are different.
I believe the new site design allows us flexibility in aspect ratio, so we could lift that restriction while we're at it (and perhaps also allow entries to start at larger sizes). We could also look at doing the theme idea finally.
I believe that this approach will help build up a community of practice interested in thinking and talking about photography and photographs, not just camera gear and optical mechanics.
What do you all think?