Simple, drop the harvest to a sustainable number (whatever that is). Go catch salmon.
Rather ironic that you can't understand other communities deal with pressure and limitations on there available resources. Instead of getting something for free, you should have to consider a counterbalance. You get to further deplete the unsustainable deer (your argument) locally available to you, so you should not get to deplete other meat resources outside of your GMU.
Or, is your argument that the way of life in rural communities is jetting around the state to kill and fly meat back?
Subsistence should require something to insure it is not abused by those who don't need it. Something not monetary that those who actually need it will not struggle under and to avoid the messy business of trying to decide who does or does not actually deserve it through things like income requirements.