Not really sure about the best way to solve this particular quandary, but perhaps having each contest last a shorter time before vote would result in slightly fewer entries per contest? While it is only lovely to have a flood of entries for a contest, it is harder to finish one contest with such numbers.

Alternatively, one could have each contest operate in "rounds"... Say, ten entries per round. If a theme is especially popular, you have more rounds for it, say up to three or four rounds. Perhaps top three from each should go on to "theme finale"?

Having shorter rounds might make things go faster. It's far easier to pick the best of ten than to pick the best of fifty.

Of course the above might be overly convoluted.

Part of the reason for the suggestions above, beyond the obvious of wanting to make this easier, is that we're looking forward to other contests, as we'd love to participate, but theme #1 was not something that sparked our muse.