I, as a quilter, love and appreciate hand made gifts of all kinds. Unfortunately, not everyone does though, which is what would make this request so hard if given to me.
I like the Project Linus idea. We have all seen places where donors are honored by putting their name on a brick or bench, etc. And, we all know blankies are better than bricks!
Maybe the charity or hospital has a seal, emblem or moto that could be digitized and applied to an item. I like the idea of the wine bag or gift bag of chocolates. What about a golf club cover, sock thing? At that level, I'm sure there is some time being spent on the golf course. (but I see these ideas as being disposable and therefore maybe a waste of time and resources) Or, what about using the selected design to create a special 'certificate' that could be framed to hang on the wall? It would be something unique and eye catching on their brag wall. (maybe less likely to be thrown away or sent to GW)
Good luck, this is not an easy task to find an answer to. But, I'm sure the wonderful members of the QB will be able to help.