When do you intend to plant a crop(s) in your garden? Next spring?
If next spring, I would mow (with a mulching mower) what you have soon, replant the winter rye (assuming it is probably gone by now...but if not proceed) over the crimson, and let it all ride until next spring and mow all it again (this time short) and then till it before planting. You should have an excellent plot ready to grow stuff.
To be sure, last thing I would do before planting next spring (and after it has been tilled and the cover assimilated into the garden soil) get a soil test to see exactly where you are.