Two dishes into one box is easy. A diseqc switch does it all. One dish into two receivers is more difficult, as an LNB can only be allowed to see one powered receiver at a time. One box has to be connected, and one shut right off, so you're talking an A/B switch. That in itself will reduce the signal slightly.
I think your best bet is to have your minidish connected to your Sly setup downstairs, and your hotbird dish connected to whatever you're running upstairs. Simple, clean and truly independant. If you want to hook up your Sly dish upstairs too, then a twin LNB on your minidish will feed one coax downstairs, and another upstairs, but then you have yet another cable.