Hi Stew and welcome to the forum,
Yes it sometimes feels like I am repeating myself but…. as you know, every situation is different of soil, climate and weeds above all. Hence sometimes the advice is different and seems contradictory to other advice!
I have a similar predicament here with a large patch of couch, in fact I am not exactly sure how large without digging holes everywhere, but a lot of it is where my greenhouse is going!
Usually I advise a year of black polythene or possibly Mypex (I have not used it and it lets a little light through, have others found it effective against thick couch grass?) to be sure that all the couch is starved of light for long enough that roots keep growing in the dark, until exhausting their reserves of food – which takes many months, if not a year or even more sometimes.
If you buy any kind of weed suppressing membrane, the cost can be high but they can be reused. If you plant through Mypex, just be sure to burn holes not cut them, to avoid shredding of fibres. Or use landscape fabric which you can cut through and is cheaper.
The point about cardboard is valid, it will stop couch shoots pushing upwards for a month or two but as it is moist and soft when buried, the barrier effect soon passes. It is more effective on top but that is not practical on windy sites of for growing many vegetables.
If your beds are to have wooden sides, one idea is to lay Mypex in strips where your paths will be, then place the wooden sides along its edges and fill the beds – which do not have Mypex under tham. You absolutely have to kill couch in paths as well as beds. Any couch growing through the bed’s contents needs continual pulling or trowelling out and should be mostly gone within a year. Or you could lay Mypex or fabric on the beds’ surface and plant through that, maybe keep one bed with no cover on top, for sowing carrots etc.
Your first year will be the most difficult but rewards are high once your soil is clean. Keep us posted with progress!