Maybe an online survey to piggyback an online petition? I know it'd be easy to send a link to many people to fill out the survey, and you can gather a background of each hunter as well as their beliefs.
Surveymonkey is online and free; I used it for a project in college to have people rate a product idea. You could offer a list of questions, and a ranking system so the data could be analyzed. Ie- Question 1. Do you deer hunt Y/N 2. Do you want to see more deer while deer hunting Y/N. 3. On average, how many days a year do you hunt 1-2/3-5/6-10/11-20/21+ 4. What method of hunting do you use Bow/Rifle/Muzzy/All 5. Are you satisfied with the state of the current deer herd Y/N. 6. On average how much money do you spend each year on deer hunting? $0/$1-$50/$51-100/101-200/201-500/501-1000/1000+ 7. Did you harvest a deer in MN in 2013 Y/N
With this data you could present it and show how pathetic deer numbers are by how many days each hunter spends in the stand, and the relationship to deer sightings and the economic impact of these hunters.
The number crunching might get involved, but it may segment hunter groups and really show that people that spend more time on stand are seeing less deer, and success is based on increased hours spent on stand and money invested into habitat projects as opposed to deer numbers being adequate.
Maybe I'm thinking along the wrong lines though? It'll give more insight to the situation with data to support the signatures.
I'd be in favor of a petition, or both. I'd send the link all over work, and all my friends and family who are deer hunters.
Don't just focus on how effective, but rather how effective vs how much time it would take to get it done. I don't imagine it'd be hard at all. Users can help it go viral.
Zone you hunt
How many hours did you hunt last year
How many deer did you see
What is your opinion of the status deer population in your area compared to the historical average (5 very high to 1 very low)
Do you support an audit of how deer are currently managed in MN