Welcome to Missouri Clipz. There are a lot of excellent public hunting areas throughout the state. In fact a lot of them have food plots that the conservation dept puts in. Mostly a mix of different grains and such to attract anything from birds to deer.
I am not sure where you found your information about the tree stands, but almost every conservation area allows unattended portable stands. The link below has the regulation regarding the areas. Now, with that said, you need to look at the specific rules of each area. But, generally, you may leave a stand unattended as long as you label it. There are no screws, nails, etc allowed though.
If you do decide to that route, make sure you double lock with quality cable. Also, get a good set of tree sticks so you can remove those at the end of the hunt. Make the stand harder to get to by potential thieves.
Also I wouldn't just leave it all season. If you know you won't be hunting for a few weeks, just remove it and put it back prior to hunting.
The second link has all the department areas. Most allow archery or muzzleloader hunting and you can find good maps with walk in trails and such. Make sure you scout the area though. I've seen where they move plots or cleared them once done.
I hope you enjoy hunting public grounds here. There are a lot of them and a lot of good bucks have been harvested from them.
http://www.sos.mo.gov/adrules/csr/cu...-11.pdf#page=6
http://mdc4.mdc.mo.gov/applications/...st&txtAreaNm=s