I like your idea. May we consider different itteration, or addition to the idea.
With the proposal of exotic super dense entities like quark stars and others including black holes, matter on the atomic level can, and most likely does, break down to its most simplist building blocks (photons, leptons, quarks, etc). Since a black hole is proposed to be infinitely dense and occupying a zero-point in space (singularity), if the matter it sucked in was being ejected elsewhere, wouldn't it make since that what was being ejected was in the form of these most basic building blocks? Is it not also possible that the most massive of black holes may have the ability to tear these most basic of build blocks apart into pure energy?
Considering those questions, and assuming the answers are yes, then what you are introducing at the "White Hole" points in space is raw energy, which it would make since at its own "negative singulary", if you would allow me to us the term, would be just as powerful as the singularity at the center (or near center) of a black hole.
No matter how many points of exit you would have from a black hole, dividing infinity by how ever many points of exit you have is still infinity. This leads me to conclude 1 of 2 possibilities: 1) Your proposal can not exist 2) Black Holes are indeed NOT infinitely dense and DO occupy a portion of space.
Now that I think of it, there is another set of possibilities. If a black hole is indeed infinitely dense occupying a zero-point in space, and it is ejecting the material it sucks in, there must be an infinite amount of "white holes" in space as well and an infinitely dense zero-point white hole. You could then infer any or all of the following: 1) the Universe is infinite 2) the Universe has been and always will be (I personally don't like this idea) 3) White holes don't exist at all and the energy by a black hole is either contained within the event horizon or deconstructed to its most simplist form and eject back out of the black hole in a form not yet detected (maybe Hawking Radiation or variation there of).
Let me know what you think.