Posted: 01/04/2016 at 15:14
I have this stuff creeping in every year from the surrounding fields. It can be a nightmare when entangled in teh roots of treasures. In your case, I would be tempted to do as you suggest and remove all the plants you want to keep - toddler paddling pools come in handy for storing them while you clean the beds as well as plastic salad and veg crates if your supermarket/grocer will give or sell them to you.
Then spray what's left with a glyphosate based product and be prepared to do this twice or thrice to be sure you've got it. Do it on a sunny day when winds are light or non existent and rain is not expected for at least 6 hours. It takes 2 weeks for each application to work.
Meanwhile, wash the roots of your treasures, one bucketful at a time and pick out the last scrap of couch grass before potting up in pots or troughs. Use a fork rather than a spade to dig them out if you can as this creates fewer new root cuttings of the nasties. Take the opportunity to divide and multiply any decent sized specimens.