Don't really understand the problem. If you have any kind of strobe fitted with a spill kill (small deep reflector, 21 cm diameter with many systems), you can fit a soft box of any desired size - usually accessories like soft boxes are available with fittings ("speed rings") to fit different diameters of reflectors. You can of course also fit an umbrella, the only downside is that it is then harder to control spill, but not impossible using flags (pieces of black card taped to other lighting stands and positioned as appropriate).
It is slightly harder to get the light right over the center of your set - the only way you're going to do this is with a stand off to one side with a long boom arm which you would position possibly at 45 degrees or flatter and to which you can fix a counterweight - obviously if the counterweight is as far from the center as the flash head, it needs to weigh the same, if it can be twice as far away, it only needs to be half as heavy. The stand you put all this on needs to be strong, since it needs to carry the flash head plus the counterweight plus the boom arm. Don't try a setup without a counterweight, it will collapse for sure! An overhead softbox is quite a standard setup for lighting still lives, so it's not too much of a problem to produce!
Regards,
David
PS: A simpler but less easily adjustable rig would of course be two lighting stands, one either side of the set, with a wood batten running between them and the softbox suspended from this. This will require 2 people to adjust but has the advantages that it doesn't stick out so far at the sides!