Catrin, manure does not scorch, perhaps fresh chicken manure might. Look at fields where animals poo, and the lush growth of grass.
For your couch I would cover with thick cardboard, some old manure (compost) on top.Then more cardboard in 2-3 months time, maybe a third layer in mid summer.
Or membrane, after applying compost. But that will involve a lot of cutting around the bushes.
For raspberries, mulch almost all the area except the original clumps.
You need persistence this year and commitment to remove all regrowth of couch near the woody stems of your bushes.