I sow winter rye nearly every fall and till in in the spring. In my case I have to till in 3-4 weeks before I intend to plant my garden (around Memorial Day here in CNY), giving it a chance to break down. In your case, you want the greatest bio-mass so I would let it grow until seed heads begin to form. You will likely need to cut it before tilling it under (otherwise it tangles in the tines).
If you're looking for further soil improvement and to beat weeds, consider a couple of crops of buckwheat this season to till under as well. For buckwheat, when it flowers, let the
bees work it for a few days, then cut and/or till under. Wait a week or so to plant a 2nd crop of buckwheat and repeat...then you can plant another cover crop (winter rye, hairy vetch, etc.) for the winter. By next spring, you should have enriched soil with much more tilth.
Another option for winter is to till in and pile on the leaves as cover. Leaves provide organic matter and minerals 'mined' from deep in the soil.
(One fall I piled leaves inside a 12' ring of snow
fence in my garden. The following spring as I tilled, when I got to that spot, the tiller sank effortlessly to it's maximum depth. The soil life (critters) had tilled for me [which is why/how no till can be so effective]).
Best wishes for success,
-Mike