Late Aug - mid September is the recommended planting date for the radishes in our area. They sprout and grow very fast, the seed is about 3x the size of turnips and easier to plant IMO. They need about 60 lbs. of actual nitrogen per acre for best growth also.
Nothing wrong with growing the Trophy radishes, I'd grow those before going to much trouble looking for the cheaper options.
Honestly Mike, not much ground prep is needed with the radish. If you could spread the fertilize and disk that in followed by spreading the seed and packing is all that's needed. I know where a small 3 point hitch disk is located if you might be interested. I haven't looked at it close and don't know what the man wants for it, but I'm sure it would be less than you paid to fix that tiller