But given that I have no idea what I want, I figure the more people I invite to provide ideas the better.
You can just do what Steve Jobs did with Next: pick a designer you like, and leave it entirely up to him.
Ironically not because Jobs didn't have ideas on what he wanted but because the designer insisted:
"I asked him if he would come up with a few options, and he said, 'No, I will solve your problem for you and you will pay me. You don’t have to use the solution. If you want options go talk to other people.'"