Two beds of 1.5x8m can grow you a lot of food and you can sow carrot, parsnip there, asap. Concentrate on doing them well, this year.
Your mulched/carpeted area could grow leeks, cucurbits, perhaps large brassicas such as Brussels sprouts – planted through the mulch.
For the rest, leave it covered all year. You can’t cure a massive amount of perennial weeds in weeks, unless you want to be at them with a trowel for many hours, much easier to leave them in the dark until winter.
