I don't see how I can take a private address I've been assigned for my home network and legitimately use it on our work network.

Right, that's the point I'm trying to make. You're under the illusion that the addresses are something special when they're not. You can legitimately do what I'm talking about, and it's no big deal at all and no one will notice and there will be no conflicts. I'll try to explain how it works in my next post...