I think Sam is on the right track for sure.
Anytime you run a contest the people that want to enter need to believe that they have a chance of winning if they are to stay involved or enter, especially if there is a entry fee of some kind.
Most guys do not believe they are going to kill the biggest deer next year to win the mount, just a fact of life rather it be land available to hunt, time, interest, whatever.
If you run a contest that had a minimum size or score or points, something, to qualify to put them in a drawing to win a free mount you would generate a lot more interest I think.
As I'm sure you know some guys that mount a 120 class buck as just as proud of it as someone that mounts their 170.
The more you spread the love and give more opportunity to win the more participation and excitment you can generate.
I created a different format for walleye tournament on Erie some years ago. I went away from the "pro" type competition, payed out a ton of places rather than making it the traditional top heavy payout and changed the team format. What the traditional walleye tourney guys said wouldn't work because they could not draw 35 boats to a tourney. We were able to fill out the max field of 110 boats. The 6th and last year I held it we sold out the 110 boat field in 22 hrs from when entry opened.
I guess that is a long winded way of saying give more opportunity to win other than the old biggest deer stuff like everyone else.