The aperture/flash ambient/shutter speed rule is most useful when balancing or manipulating ratios outdoors. If you have the power to spare in your studio strobes, you can set them brighter and the f stop/iso smaller/lower. You have to watch the distance to the background with broad light sources such as umbrellas. (there will be more light to bounce around) With a very directional source such as a snoot or grid, it's a lot easier to get the flash/camera exposure in a completely different realm than the indoor ambient light without a lot of spill.
So, as others have said, first thing, set max sync. second thing iso low power high on the light, (the power of your hotshoe flash may be a limiting factor here) The softbox is sort of the middle in terms of directionality. As has been said, take care to angle the light and reflector so that light strikes the subject only. Move the subject/main/reflector away from the wall. Lastly, stop down your aperture and correspondingly increase the output of your flash. (once again, studio strobes even 200ws models are looking better and better here)
Also, it's not cheating to hang a black sheet to tip the balance. If you do all of the things suggested in this thread, it'll be a 90% lighting solution, If you need to change the background from, say a white wall to a white wall with a black sheet... hey whatever works!