Yes I would do exactly that. You could remove some suckering raspberry roots to plant in another, clean bed. Meanwhile the mulching is well worth it compared with weeding couch grass every year, as you would never be able to remove more than a half of its roots.
And yes black polythene makes most sense, well secured/weighted at the edges as the raspberries will push it up at first, until they run out of reserves, as the couch grass also exhausts itself, over the course of a whole season: it should be 95% gone by winter. Then any remaining roots can be pulled out or levered out with a trowel, and keep an eye out for a few stragglers in 2013 to have soil 100% clear.