You could cover some of it with heavy duty black sheet mulch, weighed down well and just leave it.
That's more or less what I did on about half of my plot when I first got it. I made raised beds using wood from skips or pallets, then cut & removed the plastic from inside the frame work and did a rough dig turning the clod over - yes, with all the grass and perennial weed roots still there - and topped up with compost/manure. The idea of the dig is to break up the compacted soil as the plot was prone to flooding in very wet seasons so digging allowed water to drain away, and raised beds added height and hence gravity. I covered each bed first with sheets of cardboard (supermarkets are a good source) and over that, with a weed suppressant sheet (I got cheap perforated black plastic sheeting rather than the expensive fabric one) and stapled it down on the wood frames. Presto, instant beds - the cardboard prevent light from reaching weed seeds and grass, the manure and compost added nutrients. The remaining heavy duty black plastic smothered the grass on the footpaths.
This method is ideal for summer crops such as sweetcorn, courgettes & all winter squashes because the black plastic warms the soil and as most of these were not planted out until early-mid June, the weeds and grass were kept smothered. Simply make planting holes through the plastic/cardboard and back fill with compost (use any card/plastic offcuts as collars round the plants to prevent weeds from pushing up with your crop). The cardboard acts like a mulch and prevents water loss, and the perforated weed suppressant allowed rain water to penetrate so watering issues should be minimal.
This method however is not ideal for root crops like carrot and parsnip, and the black plastic can make the soil too warm for crops such as peas and broad beans which prefer cooler conditions.
Downside are hiding places for slugs and snails so do consider methods of dealing with them - I sprinkled a handful of slug pellets on the soil before covering the bed with the cardboard. Another downside is that some weeds will find their way through holes in the plastic - bindweed are extremely good at this. You could use weedkiller on those weeds without having to treat the whole plot.
At the end of the season, remove the weed suppressant sheeting. Most of the cardboard will probably have rotted. When digging the bed over, the compost and manure should help to break up the earlier clods of clay soil and you should then be able to remove the roots more easily - couch grass roots can remain dormant for more than a year so don't be fooled and think they are dead!
For a short term method, this worked well and helped me to plant up the plot in the first year without using too much weedkiller, or spend all my time digging the weeds out before planting up. I've still got raised beds (been a godsend with this year's wet weather!) but you could easily dismantle the beds after a couple of years and remove the plastic sheeting on the footpaths if you preferred not to have static beds and wanted to cultivate the whole plot.