Here is another to look at:
RSMO 537.294I agree the local sheriff would have the most insight.
It seems long as you are shooting in a responsible manner (proper backstop, etc), not violating the unlawful use of a weapon statute, aren't a convicted felon, and on private property not subject to ordinances in place by a city or a county, it is legal.
I've never seen a Missouri law that stated a minimum number of acres to have a range.
Another source could be the Department of Conservation if you run across one of them before getting to the Sheriff.