Thank you for passing this on. It will certainly be something I'll watch for and will learn from your experience. Sorry you had to go through this. Just don't feel alone.
A sick hen doesn't move around very much. I keep my hospital cases in a blanket lined laundry basket with Scott towels or puppy pads under them. They don't go anywhere, gives them a chance to look around, and much easier to feed them, (avoiding the lap spills you mention).
I think you're doing...