cover cropping in perennial beds

this might be a silly question, but I've got some perennial herbs (thyme, rosemary, yarrow, etc) and want to cover the soil when they are dormant.

I'm in western north carolina (zone 6b) and I've got the following cover crop seeds to choose from:

rye
winter wheat
barley
oat/pea mix
fava

the thing I'm having trouble wrapping my head around is the planting time for my cover crops is now, but my herbs are still big and full...should I undersow the cover crops under the herbs? perhaps put them in rows directly next to the herbs?

and then what happens in spring?

Just having trouble wrapping my head around my plan.

I would just use mulch. The cover crops would be a lot of competition .

I would try something shorter than the herbs. Maybe Corsican Mint or Creeping Thyme? Even when those are dormant, they cover the soil pretty well.

My zone is a little warmer and my herbs are in containers that I can move to best locations with the seasons. My goal is to feed the soil microbes during the cool season and get an additional production from the containers. What works for me is top multiplying onions. As the sets mature on the top of the onions I plant them around my herbs and they grow all winter supplying green onions. during the summer I have alpine strawberries.