Hi Eliza
I am no expert but my guess is that you are trying to fit too much into a small area. You can Google planting distances for blackcurrants and raspberries which will give an idea about likely spread. Autumn raspberries are notorious for spreading laterally and you might well end up with a thicket of canes in the middle of your currant. There is room for only one plant or row in a standard 1.2 wide metre raised bed with paths either side. I think it is too late to prune to the base, but perhaps others have a different view.
Here is a photo of a single blackcurrant and autumn raspberry canes planted in the winter.
John