My mother and dad always had a large patch raspberries, but they kept them in rows tied to wire stretched between strong stakes. By doing this you can control the width of the rows by constant hoeing off the new shoots that come up out of the row, or dig them and sell or give them away. It's not too hard to keep them in check if you are diligent in either tilling between the rows or hoeing deep enough to stop the underground roots from spreading out. If you get down and dirty with your raspberries that are running into your strawberries, dig deep enough to get the runners, then keep a path of at least a foot clear of new shoots you shouldn't have to move the strawberries.

My father was merciless between the raspberry rows with the rototiller. He grew strawberries too, and kept at least a 3-foot rototilled area between the strawberries and the raspberries. He would "sift" the rototilled area with a hay fork to remove roots and shoots cut off in the process. And, as Rachel suggested, he grew raspberries trained on wire and stakes.

He grew and sold berries for 66 of the 85 years of his life and I've found his techniques and advice are sound.

Kate

I don't use a tiller- I just keep a fork or spade around to lift the run-away offenders- or "root prune" by stomping on the shovel down a line cutting an edge. It is the same effect- just manual labor. Saves on prep time- and clean-up is much easier! If you find the canes coming up in a place you cant lift them without damaging surrounding crops- use an old fashioned Dandilion puller- or long screwdriver and extract as much of the cane as you can. The root will eventually die if it is not being nourished with sunlight.
Best of luck to your berries!
Julie