I'm thinking the best way will probably be to go for the group stage + knockout format. Groups of 4 and we can continue to add groups as per demand for entrants.
Taking into account concerns about interest waning if the comp was long, my suggested comp format would be:
Groups of 4 with one match-up against each opponent in each group - Guarantees each entrant at least 3 designs. Number of groups determined by how many entrants we get.
2 Options for who progresses.
Option 1: Top 2 from each group progress + next best if required to make up 8, 16, 32 etc for knockout round.
Option 2: Winner of each group progresses plus however many required for knockout round judged on Votes Difference (Votes For - Votes Against).
In order to ensure no bias in voting, you can't vote on match-ups within your own group.