I have allowed WR to mature, then knocked it flat and lightly disced it in. That is WAY too much seed! If you let the seed heads mature, it's fine to mow it or roll it down; you won't get too much germination, like you would if you disced it.
If I was going to plant a summer crop of BW and sunflower, I wouldn't wait until the rye seed hardened off. I'd broadcast the BW at about 25#/acre (50 is fine for a monoculture, but too much if mixed with other stuff) and the 50# of SF/birdseed, along with as much lime as you can justify. Then, I'd mow or (preferably) roll the rye stems down on top of what you broadcast. Get fancy and include 2# of chicory in case you have an especially hot and dry summer.
Good luck and take pictures! We all like pictures.