For many years oats has been drilled along with alfalfa seed, as a nurse crop to control weed pressure.
I don't see why it wouldn't work using oats and the grass seed/seeds of your choice instead of alfalfa.
Instead of drilling we till a smooth seed bed and broadcast oats, alfalfa, tall fescue and orchard grass all mixed
into dry fertilizer as the carrier. After broadcasting the mix we drag the field for good soil to seed contact.
We cut the field when the oats is in boot stage and either chop it for oatlage or bale it as baleage.
In Minnesota we like to seed the 1st week of April, I assume NE Missouri might be a couple weeks earlier.
A heavy stand of oats can be difficult to dry for baling, but a light seeding of 1 bushel per acre would be enough to
crowd out early weeds and dry down better for baling. Or you could use an early maturing oats to combine for grain
and bale the straw for bedding. In either case a variety shorter in height would be preferred over tall varieties.