RE: Hunting in the off season....
You may have trouble finding a place that has exotics that isn't fenced in. Those animals cost money to import and no one would want to see their investments walk off.
Most of the exotics are taken for the mounts anyway. The meat from most is not good tablefare, with the exception of some of the small deer variations.
If you do find a place please post it up for the rest.
Good Hunting,