End of Sep or Oct is too late for turnips or radishes.  Even labor day is too late for turnips.  They will give some tops, but not enough time for a bulb to develope.  Oats may work, but they will freeze unless you use a winter oat.  Rye would grow longer in the fall, give some good grazing, but going with corn the next year, may not be the best.
If you can get radishes or turnips flown on in early Aug would be best.  That would work, but the key here is to get the stuff sown well before labor day