So if you're coming off of mature rye right now, you want to start the process of killing it off and leaving a clean seed bed. Several ways to do that. Is there seed on there yet or no? Basically, if may take you a little time but you wanna start the mowing & killing process (you may have a couple round-up applications needed) so you can put as much of that as you want into purple top turnips & Radishes (daikon, tillage, ground hog - all the same). They will go in ground July 20 - August 15 at the latest. They need a clean seed bed and you likely will need to hit that portion with clethodim & crop oil about 2-3 weeks after planting or when you notice any grasses or rye competing with them.
The portion you would like to continue rye - you have lots of options there as well. If you wanted to do it just winging it and ok with heavy seed, just work it all up again with the seed there and add some clover, winter peas & small amount of radish to that mix and have that completed Aug 25-Sept 10.